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Sets EXERCISE 1.5 Solutions
- Q1(i): Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{ 1, 2, 3, 4\}$, $B = \{ 2, 4, 6, 8 \}$ and $C = \{ 3, 4, 5, 6 \}$. Find (i) A′
- Q1(ii): Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{ 1, 2, 3, 4\}$, $B = \{ 2, 4, 6, 8 \}$ and $C = \{ 3, 4, 5, 6 \}$. Find (ii) B′
- Q1(iii): Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{ 1, 2, 3, 4\}$, $B = \{ 2, 4, 6, 8 \}$ and $C = \{ 3, 4, 5, 6 \}$. Find (iii) $(A \cup C)′$
- Q1(iv): Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{ 1, 2, 3, 4\}$, $B = \{ 2, 4, 6, 8 \}$ and $C = \{ 3, 4, 5, 6 \}$. Find (iv) $(A \cup B)′$
- Q1(v): Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{ 1, 2, 3, 4\}$, $B = \{ 2, 4, 6, 8 \}$ and $C = \{ 3, 4, 5, 6 \}$. Find (v) $(A′)′$
- Q1(vi): Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{ 1, 2, 3, 4\}$, $B = \{ 2, 4, 6, 8 \}$ and $C = \{ 3, 4, 5, 6 \}$. Find (vi) $(B – C)′$
- Q2(i): If $U = \{ a, b, c, d, e, f, g, h\}$, find the complements of the following sets : (i) $A = \{a, b, c\}$
- Q2(ii): If $U = \{ a, b, c, d, e, f, g, h\}$, find the complements of the following sets : (ii) $B = \{d, e, f, g\}$
- Q2(iii): If $U = \{ a, b, c, d, e, f, g, h\}$, find the complements of the following sets : (iii) $C = \{a, c, e, g\}$
- Q2(iv): If $U = \{ a, b, c, d, e, f, g, h\}$, find the complements of the following sets : (iv) $D = \{ f, g, h, a\}$
- Q3(i): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) $\{x : x$ is an even natural number\}
- Q3(ii): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (ii) $\{ x : x$ is an odd natural number \}
- Q3(iii): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (iii) $\{x : x$ is a positive multiple of 3\}
- Q3(iv): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (iv) $\{ x : x$ is a prime number \}
- Q3(ix): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (ix) $\{ x : 2x + 5 = 9\}$
- Q3(v): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (v) $\{x : x$ is a natural number divisible by 3 and 5\}
- Q3(vi): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (vi) $\{ x : x$ is a perfect square \}
- Q3(vii): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (vii) $\{ x : x$ is a perfect cube\}
- Q3(viii): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (viii) $\{ x : x + 5 = 8 \}$
- Q3(x): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (x) $\{ x : x \ge 7 \}$
- Q3(xi): Taking the set of natural numbers as the universal set, write down the complements of the following sets: (xi) $\{ x : x \in N$ and $2x + 1 > 10 \}$
- Q4(i): If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{2, 4, 6, 8\}$ and $B = \{ 2, 3, 5, 7\}$. Verify that (i) $(A \cup B)′ = A′ \cap B′$
- Q4(ii): If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9 \}$, $A = \{2, 4, 6, 8\}$ and $B = \{ 2, 3, 5, 7\}$. Verify that (ii) $(A \cap B)′ = A′ \cup B′$
- Q5(i): Draw appropriate Venn diagram for each of the following : (i) $(A \cup B)′$
- Q5(ii): Draw appropriate Venn diagram for each of the following : (ii) $A′ \cap B′$
- Q5(iii): Draw appropriate Venn diagram for each of the following : (iii) $(A \cap B)′$
- Q5(iv): Draw appropriate Venn diagram for each of the following : (iv) $A′ \cup B′$
- Q6: Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?
- Q7(i): Fill in the blanks to make each of the following a true statement : (i) $A \cup A′ = . . .$
- Q7(ii): Fill in the blanks to make each of the following a true statement : (ii) $\phi′ \cap A = . . .$
- Q7(iii): Fill in the blanks to make each of the following a true statement : (iii) $A \cap A′ = . . .$
- Q7(iv): Fill in the blanks to make each of the following a true statement : (iv) $U′ \cap A = . . .$
Other Exercises for CBSE - Class 11 Mathematics Sets
Chapters in CBSE - Class 11 Mathematics
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