Let A = {1, 2, 3, 4, 5}; B = {7, 9, 11, 12, 13}; C = {x : x ∈ U and x is a prime number}; D = {x : x ∈ U, x < 6} and U = {x : x ∈ N. x < 15}. State whether the following statements are True/False by giving reasons.

(a) A and B are disjoint

(b) A and C are overlapping

(c) B ⊆ C

(d) A ↔ B

(e) A = D

(f) A ⊂ C

# Let A = {1, 2, 3, 4, 5}; B = {7, 9, 11, 12, 13}; C = {x : x ∈ U and x is a prime number}; D = {x : x ∈ U, x < 6} and U = {x : x ∈ N. x < 15}

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In the given question we get,A = {1, 2, 3, 4, 5},

B = {7, 9, 11, 12, 13},

C = {2, 3, 5, 7, 11, 13},

D = {1, 2, 3, 4, 5}, U = {1, 2, ….., 15}

Step by Step Explanation :(a) A and B are disjoint= This statement is True

(b) A and C are overlapping= Since, 7, 13, 11 are common element that’s why B and C are overlapping.

So, this statement is true.

(c) B ⊆ C= Since, the elements 12, 9 do not belong to C.

= That’s why the statement is

false.(d) A ↔B= Since, n(A) = 5 = n(B) that’s why the statement is

true.(e) A = D= Since, A ={1, 2, 3, 4, 5} = D that’s why the statement is

true.(f) A ⊂ C= Since, 4 ∈ A but 4 ∉ C, that’s why A ⊄ C. The statement is

false.