{"id":4070,"date":"2023-12-14T07:22:23","date_gmt":"2023-12-14T01:52:23","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=4070"},"modified":"2023-12-15T17:26:30","modified_gmt":"2023-12-15T11:56:30","slug":"samacheer-kalvi-12th-maths-solutions-chapter-12-ex-12-2","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-solutions-chapter-12-ex-12-2\/","title":{"rendered":"Samacheer Kalvi 12th Maths Solutions Chapter 12 Discrete Mathematics Ex 12.2"},"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 12.2<\/h2>\n

Question 1.
\nLet p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing each of the following statements.
\n\"Samacheer
\nSolution:
\n(i) \\(\\neg p\\) : Jupiter is not a planet
\n(ii) \\(p \\wedge \\neg q\\) : Jupiter is not a planet and India is not an island
\n(iii) \\(\\neg p \\vee q\\) : Jupiter is not a planet or India is an island.
\n(iv) \\(p \\rightarrow \\neg q\\) : If Jupiter is a planet then India is not an island
\n(v) \\(p \\leftrightarrow q\\) : If Jupiter is a planet if and only if India is an island<\/p>\n

Question 2.
\nWrite each of the following sentences in symbolic form using statement variables p and q.
\n(i) 19 is not a prime number and all the angles of a triangle are equal.
\n(ii) 19 is a prime number or all the angles of a triangle are not equal
\n(iii) 19 is a prime number and all the angles of a triangle are equal
\n(iv) 19 is not a prime number
\nSolution:
\np : 19 is a prime number
\nq : All the angles of a triangle are equal
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nDetermine the truth value of each of the following statements
\n(i) If 6 + 2 = 5 , then the milk is white.
\n(ii) China is in Europe or \\(\\sqrt{3}\\) is an integer
\n(iii) It is not true that 5 + 5 = 9 or Earth is a planet
\n(iv) 11 is a prime number and all the sides of a rectangle are equal
\nSolution:
\n\"Samacheer<\/p>\n

Question 4.
\nWhich one of the following sentences is a proposition?
\n(i) 4 + 7 = 12
\n(ii) What are you doing?
\n(iii) 3n<\/sup> \u2264 81, n \u2208 N
\n(iv) Peacock is our national bird
\n(v) How tall this mountain is!
\nSolution:
\n(i) is a proposition
\n(ii) not a proposition
\n(iii) is a proposition
\n(iv) is a proposition
\n(v) not a proposition<\/p>\n

Question 5.
\nWrite the converse, inverse, and contrapositive of each of the following implication.
\n(i) If x and y are numbers such that x = y, then x2<\/sup> = y2<\/sup>
\n(ii) If a quadrilateral is a square then it is a rectangle
\nSolution:
\n(i) Converse: If x and y are numbers such that x2<\/sup> = y2<\/sup> then x = y.
\nInverse: If x and y are numbers such that x \u2260 y then x2<\/sup> \u2260 y2<\/sup>.
\nContrapositive : If x and v are numbers such that x2<\/sup> \u2260 y2<\/sup> then x \u2260 y.<\/p>\n

(ii) Converse: If a quadrilateral is a rectangle then it is a square.
\nInverse: If a quadrilateral is not a square then it is not a rectangle.
\nContrapositive : If a quadrilateral is not a rectangle then it is not a square.<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nConstruct the truth table for the following statements.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 7.
\nVerify whether the following compound propositions are tautologies or contradictions or contingency
\n\"Samacheer
\nSolution:
\n\"Samacheer
\nIn the above Truth table the last column entries are \u2018F\u2019. So the given propositions is a contradiction.
\n\"Samacheer
\nIn the above truth table the last column entries are \u2018T\u2019. So the given propositions is a tautology.
\n\"Samacheer
\nIn the above truth table the entries in the last column are a combination of’ T ‘ and ‘ F ‘. So the given statement is neither propositions is neither tautology nor a contradiction. It is a contingency.
\n\"Samacheer
\nThe last column entires are ‘T’. So the given proposition is a tautology.<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 9.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\nThe entries in the column corresponding to q \u279d p and \\(\\neg p \\rightarrow \\neg q\\) are identical and hence they are equivalent.<\/p>\n

Question 10.
\nShow that p \u279d q and q \u279d p are not equivalent
\nSolution:
\n\"Samacheer
\nThe entries in the column corresponding to p \u279d q and q \u279d p are not identical, hence they are not equivalent.<\/p>\n

Question 11.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 12.
\nCheck whether the statement p \u279d (q \u279d p) is a tautology or a contradiction without using the truth table.
\nSolution:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 13.
\nUsing truth table check whether the statements \"Samacheer are logically equivalent.
\nSolution:
\n\"Samacheer<\/p>\n

Question 14.
\n\"Samacheer without using truth table
\nSolution:
\n\"Samacheer<\/p>\n

Question 15.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\nThe entries in the column corresponding to \"Samacheer are identical.
\nHence they are equivalent.<\/p>\n

\"Samacheer<\/p>\n

Samacheer Kalvi 12th Maths Solutions Chapter 12 Discrete Mathematics Ex 12.2 Additional Problems<\/h3>\n

Question 1.
\nShow that \"Samacheer is a tautology.
\nSolution:
\n\"Samacheer<\/p>\n

Question 2.
\nShow that \"Samacheer is a contradiction.
\nSolution:
\n\"Samacheer<\/p>\n

Question 3.
\nUse the truth table to determine whether the statement \"Samacheer is a tautology.
\nSolution:
\n\"Samacheer
\nThe last column contains only T. \u2234 The given statement is a tautology.<\/p>\n

Question 4.
\nShow that \"Samacheer
\nSolution:
\n(i) Truth table for p \\(\\leftrightarrow\\) q
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nShow that \"Samacheer.
\nSolution:
\n\"Samacheer
\n\"Samacheer
\nThe last columns of statements (i) and (ii) are identical.
\n\"Samacheer<\/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 12.2 Question 1. Let p : Jupiter is a planet and q : India is an island be …<\/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\/4070"}],"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=4070"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4070\/revisions"}],"predecessor-version":[{"id":60138,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/4070\/revisions\/60138"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=4070"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=4070"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=4070"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}