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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.3
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
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}.
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}
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}
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}.
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}.
Question 6.
Using the set symbols, write down the expressions for the shaded region in the following
(i)
(ii)
(iii)
Solution:
(i) X – Y
(ii) (X ∪ Y)’
(iii) (X – Y) ∪ (X – Y)
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
(ii) A ∩ B
(iii) (A ∩ B)’
(iv) (B – A)’
(v) A’ ∪ B’
(vi) A’ ∩ B’
(vii) From the diagram (iii) and (v) we observe that (A ∩ B)’ = A’ ∪ B’.
