Question

solve these and ill make u the brainliest​

Answer 1

Answer:

Question 1

(a)A = {0, 1} ⇒ P(A) = {∅, {0, 1}, {0}, {1}}  or   P(A)= {∅, A, {0}, {1}}

(b)B = {a, b, c} ⇒ P(B) =  {∅, {a, b, c}, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}  }

(c)C = {1, 2, 3, 4} ⇒ P(C) =  {∅, {1, 2, 3, 4}, {1}, {2}, {3}, {4}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 1, 3}, {2, 1, 4}, {3, 2, 4},  {4, 1, 3} }

Question 2

I) if A={1, 4, 7, 8} and B={2, 4, 6, 8}:

A∪B = {1, 2, 4, 6, 7, 8}

II) if A={3, 6, 9, 12} and B={2, 4, 6, 8}:

A∪B = {2, 3, 4, 6, 8, 9, 12}

III) if A={1, 3, 5, 7, 9} and B={1, 2, 3, 4, 5}:

A∪B = {1, 2, 3, 4, 5, 7, 9}

Question 3

A∩B = {} or ∅

A∩B = {1, 3, 5}

A∩B = {10}

Question 4

Considering: A′ = U \ A

A′ = {2, 4, 6, 8, 9, 10}

B′ = {1, 3, 5, 6, 10}

A′∪B′ = {1, 2, 3, 4, 5, 6, 8, 9, 10}

A′∩B′ = {6, 10}

(A∪B)′= U\{1, 2, 3, 4, 5, 7, 8, 9} = {6, 10}

(A∩B)′ = {1, 2, 3, 4, 5, 6, 8, 9, 10}

Answer 2

Question 1:

Write power sets of the following sets:

(a) {0,1} (b) {a,b,c} (c) {1,2,3,4}

★Answer 1★

(a) Let, the given set be A

» P(A)={ɸ, {0}, {1}, {0,1}}

(b) Let, the given set be S

» P(S)={ɸ, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b c}

(c) Let, the given set be B

» P(B)={ɸ, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}

Q2.

Find Union of A and B, if:

(i) A={1,4,7,8}; B={2,4,6,8}

(ii) A={3,6,9,12}; B={2,4,6,8}

(iii) A={1,3,5,7,9}; B={1,2,3,4,5}

★Answer 2★

(i) A ∪ B = {1,2,4,6,7,8}

(ii) A ∪ B = {2,3,4 6,8,9,12}

(iii) A ∪ B = {1,2,3,4,5,7,9}

Q3.

Find intersection of A and B, if:

(a) A={ }; B={0,1,2}

(b) A={1,2,3,4,5}; B={1,3,5,7,9}

(c) A={1,3,5,9,10}; B={2,4,6,8,10}

★Answer 3★

(a) A ∩ B = { } or ɸ

(b) A ∩ B = {1,3,5}

(c) A ∩ B = {10}

Q4.

Given:

U={1,2,3,4,5,6,7,8,9,10}; A={1,3,5,7}; & B={2,4,7,8,9}

(i) A' = {2,4,6,8,9,10}

(ii) B' = {1,3,5,6,10}

(iii) A' ∪ B' = {1,2,3,4,5,6,8,9,10}

(iv) A' ∩ B' = {6,10} [De Morgan's Law]

(v) (A ∪ B)' = {6,10} [De Morgan's Law]

(v) (A ∩ B)' = {1,2,3,4,5,6,8,9,10}