{"id":4119,"date":"2023-12-15T10:07:05","date_gmt":"2023-12-15T04:37:05","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=4119"},"modified":"2023-12-16T17:56:14","modified_gmt":"2023-12-16T12:26:14","slug":"samacheer-kalvi-12th-maths-solutions-chapter-12-ex-12-3","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-solutions-chapter-12-ex-12-3\/","title":{"rendered":"Samacheer Kalvi 12th Maths Solutions Chapter 12 Discrete Mathematics Ex 12.3"},"content":{"rendered":"

You can Download\u00a0<\/span>Samacheer Kalvi 12th Maths Book Solutions<\/a>\u00a0Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/span><\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 12 Discrete Mathematics Ex 12.3<\/h2>\n

Choose the correct or the most suitable answer from the given four alternatives.<\/span><\/p>\n

Question 1.
\nA binary operation on a set S is a function from …….
\n(a) S \u279d S
\n(b) (S \u00d7 S) \u279d S
\n(c)S \u279d (S \u00d7 S)
\n(d) (S \u00d7 S) \u279d (S \u00d7 S)
\nSolution:
\n(b) (S \u00d7 S) \u279d S<\/p>\n

Question 2.
\nSubtraction is not a binary operation in
\n(a) R
\n(b) Z
\n(c) N
\n(d) Q
\nSolution:
\n(c) N
\nHint:
\nFor example 2, 5 \u2208 N but 2 – 5 = 3 \u2209 N<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nWhich one of the following is a binary operation on N ?
\n(a) Subtraction
\n(b) Multiplication
\n(c) Division
\n(c) All the above
\nSolution:
\n(b) Multiplication<\/p>\n

Question 4.
\nIn the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R ?
\n(a) a * b = min (a.b)
\n(b) a * b = max (a, b)
\n(c) a * b = a
\n(d) a * b = ab<\/sup>
\nSolution:
\n(d) a * b = ab<\/sup>
\nHint:
\nSince -2, 1\/2 \u2208 R , but (-2)1\/2<\/sup> \u2209 R.<\/p>\n

Question 5.
\nThe operation * defined by a * b = \\(\\frac{a b}{7}\\) is not a binary operation on ……….
\n(a) Q+<\/sup>
\n(b) Z
\n(c) R
\n(c) C
\nSolution:
\n(b) Z
\nHint:
\nSince 3, 5 \u2208 Z, but \\(\\frac{3 \\times 5}{7} \\notin\\) Z.<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nSolution:
\n(b) y = \\(\\frac{-2}{3}\\)<\/p>\n

Question 7.
\nIf a * b = \\(\\sqrt{a^{2}+b^{2}}\\) on the real numbers then * is ……..
\n(a) commutative but not associative
\n(b) associative but not commutative
\n(c) both commutative and associative
\n(d) neither commutative nor associative
\nLet, a, b \u2208 R
\n\"Samacheer
\n(1) = (2) = * is associative
\nSo * is both commutative and associative
\nSolution:
\n(c) both commutative and associative<\/p>\n

Question 8.
\nWhich one of the following statements has the truth value T ?
\n(a) sin x is an even function.
\n(b) Every square matrix is non-singular
\n(c) The product of complex number and its conjugate is purely imaginary
\n(d) \\(\\sqrt{5}\\) is an irrational number
\nSolution:
\n(d) \\(\\sqrt{5}\\) is an irrational number<\/p>\n

Question 9.
\nWhich one of the following statements has truth value F ?
\n(a) Chennai is in India or \\(\\sqrt{2}\\) is an integer
\n(b) Chennai is in India or \\(\\sqrt{2}\\) is an irrational number
\n(c) Chennai is in China or \\(\\sqrt{2}\\) is an integer
\n(d) Chennai is in China or \\(\\sqrt{2}\\) is an irrational number
\nSolution:
\n(c) Chennai is in China or \\(\\sqrt{2}\\) is an integer<\/p>\n

Question 10.
\nIf a compound statement involves 3 simple statements, then the number of rows in the truth table is ……….
\n(a) 9
\n(b) 8
\n(c) 6
\n(d) 3
\nSolution:
\n(b) 8
\nHint:
\n(i.e.) 23<\/sup> = 8<\/p>\n

Question 11.
\nWhich one is the inverse of the statement \"Samacheer
\n\"Samacheer
\nSolution:
\n(a) \\((\\neg p \\wedge \\neg q) \\rightarrow(\\neg p \\vee \\neg q)\\)<\/p>\n

Question 12.
\nWhich one is the contrapositive of the statement \\((p \\vee q) \\rightarrow r\\)?
\n\"Samacheer
\nSolution:
\n(a) \\(\\neg r \\rightarrow(\\neg p \\wedge \\neg q)\\)<\/p>\n

\"Samacheer<\/p>\n

Question 13.
\nThe truth table for \\((p \\wedge q) \\vee \\neg q\\) is given below
\n\"Samacheer
\nWhich one of the following is true?
\n\"Samacheer
\nHint: The truth table for \\((p \\wedge q) \\vee \\neg q\\)
\n\"Samacheer
\nSolution:
\n(3) T T F T<\/p>\n

Question 14.
\nIn the last column of the truth table for \\(\\neg(p \\vee \\neg q)\\) the number of final outcomes of the truth value ‘F’ are
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nHint:
\nThe truth table for \\(\\neg(p \\vee \\neg q)\\)
\n\"Samacheer
\nSolution:
\n(c) 3<\/p>\n

Question 15.
\nWhich one of the following is incorrect? For any two propositions p and q, we have …….
\n\"Samacheer
\nSolution:
\n(c) \\(\\neg(p \\vee q) \\equiv \\neg p \\vee \\neg q\\)<\/p>\n

Question 16.
\n\"Samacheer
\nWhich of the following is correct for the truth \\((p \\wedge q) \\rightarrow \\neg p\\) ?
\n\"Samacheer
\nHint:
\n\"Samacheer
\nSolution:
\n(2) F T T T<\/p>\n

\"Samacheer<\/p>\n

Question 17.
\n\"Samacheer
\n\"Samacheer
\nSolution:
\n(d) \\(\\neg(p \\wedge q) \\wedge | p \\wedge(p \\vee \\neg r)]\\)<\/p>\n

Question 18.
\nThe proposition \\(p \\wedge(\\neg p \\vee q)]\\) is ……..
\n(a) a tautology
\n(b) a contradiction
\n(c) logically equivalent to \\(p \\wedge q\\)
\n(d) logically equivalent to \\(p \\vee q\\)
\nSolution:
\n(c) logically equivalent to \\(p \\wedge q\\)<\/p>\n

Question 19.
\nDetermine the truth value of each of the following statements:
\n(a) 4 + 2 = 5 and 6+ 3 = 9
\n(b) 3 + 2 = 5 and 6 + 1 = 7
\n(c) 4 + 5 = 9 and 1 + 2 = 4
\n(d) 3 + 2 = 5 and 4 + 7 = 11
\n\"Samacheer
\nSolution:
\n(1) F T F T<\/p>\n

\"Samacheer<\/p>\n

Question 20.
\nWhich one of the following is not true?
\n(a) Negation of a negation of a statement is the statement itself.
\n(b) If the last column of the truth table contains only T then it is a tautology.
\n(c) If the last column of its truth table contains only F then it is a contradiction
\n(d) If p and q are any two statements then p \u27f7 q is a tautology.
\nSolution:
\n(d) If p and q are any two statements then p \u27f7 q is a tautology.<\/p>\n

Samacheer Kalvi 12th Maths Solutions Chapter 12 Discrete Mathematics Ex 12.3 Additional Problems<\/h3>\n

Choose the correct or the most suitable answer from the given four alternatives.<\/span><\/p>\n

Question 1.
\nWhich of the following are statements?
\n(i) May God bless you
\n(ii) Rose is a flower
\n(iii) milk is white
\n(iv) 1 is a prime number
\n(a) (i), (ii), (iii)
\n(b) (i), (ii), (iv)
\n(c) (i), (iii), (iv)
\n(d) (ii), (iii), (iv)
\nHint:
\nSentence (ii), (iii) and (iv) are statements
\n(ii) Rose is a flower – True
\n(iii) Milk is white – True
\n(iv) 1 is a prime number
\n\u2234 (ii), (iii), (iv) are statements
\n(i) May god bless you. This statement can not be assigned True or False.
\n\u2234 (i) is not a statements
\nSolution:
\n(d) (ii), (iii), (iv)<\/p>\n

Question 2.
\nIf a compound statement is made up of the three simple statements, then the number of rows in the truth table is …….
\n(a) 8
\n(b) 6
\n(c) 4
\n(d) 2
\nHint:
\nThe number of rows in truth table = 2n<\/sup> = 23<\/sup> = 8
\nSolution:
\n(a) 8<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nIf p is T and q is F, then which of the following have the truth value T? ………
\n\"Samacheer
\n(a) (i), (ii), (iii)
\n(b) (i), (ii), (iv)
\n(c) (i), (iii), (iv)
\n(d) (ii), (iii), (iv)
\nHint:
\np is T then ~p is F
\nq is F then ~ q is T
\n\"Samacheer
\nSolution:
\n(c) (i), (iii), (iv)<\/p>\n

Question 4.
\nThe number of rows in the truth offimg6 is ……..
\n(a) 2
\n(b) 4
\n(c) 6
\n(d) 8
\nHint:
\nNumber of simple statements given is 2. i.e., p and q.
\nNumber of rows in the truth table of \\(\\sim[p \\wedge(\\sim q)]\\) = 22<\/sup> = 4
\nSolution:
\n(b) 4<\/p>\n

Question 5.
\nThe conditional statement p \u279d q is equivalent to ……..
\n\"Samacheer
\n\"Samacheer
\nThe truth table for p \u279d q and \\((\\sim p \\vee q)\\) having the last column identical.
\n\u2234 p \u279d q is equivalent to \\((\\sim p \\vee q)\\)
\nSolution:
\n(3) \\(\\sim p \\vee q\\)<\/p>\n

Question 6.
\nWhich of the following is a tautology?
\n\"Samacheer
\nSolution:
\n(c) \\(\\boldsymbol{p} \\vee \\sim \\boldsymbol{p}\\)
\nHint:
\nA statement is said to be a tautology if the last column of its truth table contains only T.
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 7.
\nIn the set of integers with operation * defined by a * b = a + b – ab, the value of 3 * (4 * 5) is ……..
\n(a) 25
\n(b) 15
\n(c) 10
\n(d) 5
\nHint:
\na * b = a + b – ab
\n3 * (4 * 5) = 3 * (4 + 5 – 4(5))
\n= 3 * (9 – 20)
\n= 3 * (-11)
\n= 3 + (-11) – 3(-11)
\n= 3 – 11 + 33
\n= -8 + 33 = 25
\nSolution:
\n(a) 25<\/p>\n

Question 8.
\nIn the multiplicative group of cube root of unity, the order of \\(\\omega^{2}\\) is ……
\n(a) 4
\n(b) 3
\n(c) 2
\n(d) 1
\nSolution:
\n(b) 3
\nHint:
\n\"Samacheer<\/p>\n

Question 10.
\n\"Samacheer
\n(a) 5
\n(b) 5\\(\\sqrt{2}\\)
\n(c) 25
\n(d) 50
\nHint:
\n\"Samacheer
\nSolution:
\n(b) 5\\(\\sqrt{2}\\)<\/p>\n

\"Samacheer<\/p>\n

Question 11.
\nThe order of -i in the multiplicative group of 4th<\/sup> roots of unity is ……..
\n(a) 4
\n(b) 3
\n(c) 2
\n(d) 1
\nHint:
\nThe roots of fourth roots of unity are 1, -1, i, -i
\nThe identity element is 1
\n(-i)4<\/sup> = i4<\/sup> = 1
\nOrder of (-i) = 4.
\nSolution:
\n(a) 4<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download\u00a0Samacheer Kalvi 12th Maths Book Solutions\u00a0Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 12 Discrete Mathematics Ex 12.3 Choose the correct or the most suitable answer from the given four alternatives. Question 1. A binary …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[8],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4119"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=4119"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4119\/revisions"}],"predecessor-version":[{"id":60153,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4119\/revisions\/60153"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=4119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=4119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=4119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}