Question

A={x:2x+1,x€n,x<=5},B={x:x is a composite number,x<=12},then show that (AUB)-(A intersection B)=(A-B)U(B-A)​

Answer 1

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Answer 2

Answer:

Given,

A={x : 2x+1, x ∈ N, x ≤ 5 },

B={x : x is a composite number, x ≤ 12 },

Since, composite number is a positive integer which is not prime,

Thus, the roster form of the sets are,

A = {3, 5, 7, 9, 11 }

B = { 4, 6, 8, 9, 10, 12 },

A ∪ B = all elements of A and B = { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

A ∩ B = common elements of A and B = { 9 },

(A ∪ B) - (A ∩ B) = { 3, 4, 5, 6, 7, 8, 10, 11, 12 },

A - B = { 3, 5, 7, 11 },

B - A = { 4, 6, 8, 10, 12 },

( A - B ) ∪ ( B - A ) = { 3, 4, 5, 6, 7, 8, 10, 11, 12 },

⇒ (A ∪ B) - (A ∩ B) = ( A - B ) ∪ ( B - A )

Hence, proved.....