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

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

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 Samacheer Kalvi
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 Std Maths 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 Maths Set Language 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}.

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

Set Language Maths 9th Class 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 Samacheer Kalvi
(ii) A ∩ B
Kalvi Guru 9th Maths Ex 1.3
(iii) (A ∩ B)’

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

Samacheer 9th Maths Solutions Ex 1.3

Class 9th Maths Chapter 1 Exercise 1.3 Samacheer Kalvi