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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.3

9th Maths Exercise 1.3 Samacheer Kalvi Question 1.
Using the given venn diagram, write the elements of
(i) A
(ii) B
(iii) A ∪ B
(iv) A ∩ B
(v) A – B
(vi) B – A
(vii) A’
(viii) B’
(ix) U
9th Maths Exercise 1.3 Solutions Samacheer Kalvi Set Language
Solution:
(i) A = {2, 4, 7, 8, 10}
(ii) B = {3, 4, 6, 7, 9, 11}
(iii) A ∪ B = {2, 3, 4, 6, 7, 8, 9, 10, 11}
(iv) A ∩ B = {4, 7}
(v) A – B = {2, 8, 10}
(vi) B – A = {3, 6, 9, 11}
(vii) A’ = {1, 3, 6, 9, 11, 12}
(viii) B’ = {1, 2, 8, 10, 12}
(ix) U = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12}.

9th Maths Set Language Exercise 1.3 Question 2.
Find A ∪ B, A ∩ B, A – B and B – A for the following sets.
(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}
(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u]
(iii) A = {x : x ∈ N, x ≤ 10} and B = {x : x ∈ W, x < 6}
(iv) A = Set of all letters in the word “mathematics” and B = Set of all letters in the word “geometry”
Solution:
(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}
A ∪ B = {2, 6, 10, 14} ∪ {2, 5, 14, 16} = {2, 5, 6, 10, 14, 16}
A ∩ B = {2, 6, 10, 14} ∩ {2, 5, 14, 16} = {2, 14}
A – B = {2, 6, 10, 14} – {2, 5, 14, 16} = {6, 10}
B – A = {2, 5, 14, 16} – {2, 6, 10, 14}  = {5, 16}

(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}
A ∪ B = {a, b, c, e, u) ∪ {a, e, i, o, u) = {a, b, c, e, i, o, u}
A ∩ B = {a, b, c, e, u} ∩ {a, e, i, o, u} {a, e, u}
A – B = {a, b, c, e, u) – {a, e, i, o, u) = {b, c}
B – A = {a, e, i, o, u} – {a, b, c, e, u} =  {i, o}

(iii) x ∈ {1, 2, 3, ……..} ; x ∈ {0, 1, 2, 3, 4, 5, ……..}
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {0, 1, 2, 3, 4, 5}
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ∪ {0, 1, 2, 3, 4, 5} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ∩ {0, 1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
A – B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {0, 1, 2, 3, 4, 5} = {6, 7, 8, 9, 10}
B – A = {0, 1, 2, 3, 4, 5} – {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} = {0}

(iv) A= {m, a, t, h, e, i, c, s), B = {g, e, o, m, t, r, y)
A ∪ B = {m ,a, t, h, e, i, c, s} ∪ {g, e, o, m, t, r, y} = {m, a, t, h, e, i, c, s, g, o, r, y)
A ∩ B = {m, a, t, h, e, i, c, s} ∩ {g, e, o, m, t,r,y} = {m, t, e}
A – B = {m ,a, t, h, e, i, c, s} ∪ {g, e, o, m, t, r, y} = {a, h, i, c, s)
B – A = {m, a, t, h, e, i, c, 5} ∩ {g, e, o, m, t,r,y} = {g, o, r, y}

9th Std Maths Exercise 1.3 Question 3.
If U = {a, b, c, d, e,f g ,h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets.
(i) A’
(ii) B’
(iii) A’ ∪ B’
(iv) A’ ∩ B’
(v) (A ∪ B)’
(vi) (A ∩ B)’
(vii) (A’)’
(viii) (B’)’
Solution:
(i) A’ = U – A = {a, b, c, d, e, f, g, y} – {b, d, f, h} = {a, c, e, g}
(ii) B’ = U – B = {a, b, c, d, e, f, g, y) – {a, d, e, h] = {b, c, f, g}
(iii) A’ ∪ B’= {a, c, e, g} ∪ {b, c, f, g} = {a, b, c, e, f g}
(iv) A’ ∩ B’= {a, c, e, g} ∩ {b, c, f, g} = {c, g}
(v) (A ∪ B)’ = U – (A ∪ B) = {a, b, c, d, e, f, g, y) – {a, b, d, e, f, h} = {c, g}
(vi) (A ∩ B)’ = U – (A ∩B) = {a, b, c, d, e, f, g, y} – {d, h} = {a, b, c, e, f, g}
(vii) (A’)’ = U – A’ = {a, b, c, d, e, f, g, h} – {a, c, e, g} = {b, d, f, h)
(viii) (B’)’ = U – B’ = {a, b, c, d, e, f, g, h} – {b, c, f, g} = {a, d, e, h}

9th Standard Maths Exercise 1.3 Question 4.
Let U = {0, 1, 2 , 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets.
(i) A’
(ii) B’
(iii) A ‘ ∪ B’
(iv) A’ ∩ B’
(v) (A ∪ B)’
(vi) (A ∩ B)’
(vii) (A’)’
(viii) (B’)’
Solution:
(i) A’ = U – A = {0, 1 ,2, y, 4, 5, 6, 7} – {1, 3, 5, 7} = {0, 2, 4, 6}
(ii) B’ = U – B = {0, 1, 2, 3, 4, 5, 6 ,7} – {0, 2, 3, 5, 7} = {1, 4, 6}
(iii) A’ ∪ B’ = {0, 2, 4, 6} ∪ {1, 4, 6} = {0, 1, 2, 4, 6}
(iv) A’ ∩ B’ = {0, 2, 4, 6} ∩ {1, 4, 6} = {4, 6}
(v) (A ∪ B)’ = U – (A ∪ B) = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 1, 2, 3, 5, 7} = {4, 6}
(vi) (A ∩ B)’ = U – (A ∩ B)= {0, 1, 2, 3, 4, 5, 6, 7} – {3,5,7} = {0, 1, 2, 4, 6}
(vii) (A’)’ = U – A’ = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 2, 4, 6} = {1, 3, 5, 7}
(viii) (B’)’ = U – B’ = {0, 1, 2, 3, 4, 5, 6, 7} – {1, 4, 6} = {0, 2, 3, 5, 7}.

9th Maths Exercise 1.3 In Tamil Question 5.
Find the symmetric difference between the following sets.
(i) P = {2, 3, 5, 7, 11} and Q = {1, 3, 5, 11}
(ii) R = {l, m, n, o, p} and S = {j, l, n, q)
(iii) X = {5, 6, 7} and Y = {5, 7, 9, 10}
Solution:
(i) P = {2, 3, 5, 7, 11}
Q= {1, 3, 5, 11}
P – Q = {2, 3, 5, 7, 11} – {1, 3, 5, 11} = {2, 7}
Q – P = {1, 3, 5, 11} – {2, 3, 5, 7, 11} = {1}
P ∆ Q = (P – Q) ∪ (Q – P) = {2, 7} ∪ {1} = {1, 2, 7}

(ii) R = {l, m, n, o, p}
S = {j, l, n, q}
R – S = {l, m, n, o, p) – {j, l, n, q} = {m, o, p)
s – R = {j, l, n, q) – {l, m, n, o, p}= {j, q}
R ∆ S = (R – S) ∪ (S – R) = {m, o, p) ∪ {j, q} = {j, m, o, p, q)

(iii) X = {5, 6, 7}
Y = {5, 7, 9, 10}
X – Y = {5, 6, 7} – {5, 7, 9, 10} – {6}
Y – X = {5, 6, 9, 10} – {5, 6, 7} = {9, 10}
X ∆ Y = (X – Y) ∪ (Y – X) = {6} ∪ {9, 10} = {6, 9, 10}.

9th Maths 1.3 Question 6.
Using the set symbols, write down the expressions for the shaded region in the following
(i)
9th Maths Set Language Exercise 1.3 Solutions Samacheer Kalvi
(ii)
9th Std Maths Exercise 1.3 Solutions Chapter 1 Set Language Samacheer Kalvi
(iii)
9th Standard Maths Exercise 1.3 Solutions Chapter 1 Set Language Samacheer Kalvi
Solution:
(i) X – Y
(ii) (X ∪ Y)’
(iii) (X – Y) ∪ (X – Y)

9th Maths Exercise 1.3 Question 7.
Let A and B be two overlapping sets and the universal set U. Draw appropriate Venn diagram for each of the following,
(i) A ∪ B
(ii) A ∩ B
(iii) (A ∩ B)’
(iv) (B – A)’
(v) A’ ∪ B’
(vi) A’ ∩ B’
(vii)What do you observe from the diagram (iii) and (v)?
Solution:
(i) A ∪ B
9th Maths Exercise 1.3 In Tamil Solutions Chapter 1 Set Language Samacheer Kalvi
(ii) A ∩ B
9th Maths 1.3 Solutions Chapter 1 Set Language Samacheer Kalvi
(iii) (A ∩ B)’

(iv) (B – A)’
9th Maths Exercise 1.3 Solutions Chapter 1 Set Language Samacheer Kalvi
(v) A’ ∪ B’
Samacheer 9th Maths Solutions Chapter 1 Set Language Ex 1.3
(vi) A’ ∩ B’
9 Maths Samacheer Kalvi Solutions Chapter 1 Set Language Ex 1.3
(vii) From the diagram (iii) and (v) we observe that (A ∩ B)’ = A’ ∪ B’.

Samacheer Kalvi Guru 9 Maths Solutions Chapter 1 Set Language Ex 1.3

Maths Class 9 Samacheer Kalvi Solutions Chapter 1 Set Language Ex 1.3

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