Let 𝐴 and 𝐵 be sets. Using set builder notation, show that:a) 𝐴 ∩ ∅ = ∅.b) 𝐴 ∪ 𝐴 = 𝑈.c) 𝐴 ∩ (𝐵 − 𝐴) = ∅

Let 𝐴 and 𝐵 be sets. Using set builder notation, show that:a) 𝐴 ∩ ∅ = ∅.b) 𝐴 ∪ 𝐴 = 𝑈.c) 𝐴 ∩ (𝐵 − 𝐴) = ∅

Let 𝐴 and 𝐵 be sets. Show thata) (𝐴 ∩ 𝐵) ⊆ 𝐴.b) 𝐴 ⊆ (𝐴 ∪ 𝐵).c) 𝐴 − 𝐵 ⊆ 𝐴.d) 𝐴 ∩ (𝐵 − 𝐴) = ∅.e) 𝐴 ∪ (𝐵 − 𝐴) = 𝐴 ∪ 𝐵.

Let 𝐴={1,2,3,4,5,6,7,8,9}𝐴={1,2,3,4,5,6,7,8,9} and 𝐵𝐵 be the set of primes. What is |𝐴∩(ℤ−𝐵)||𝐴∩(𝑍−𝐵)|?

If  tan (A+B)=p,  tan (A−B)=q,tan (𝐴+𝐵)=𝑝,  tan (𝐴−𝐵)=𝑞, then the value of tan2A in terms of p and q is

Let f = cos2x, g = sin2x. Which of the following lie in the space spanned by f and g?Question 7Select one: 𝑁𝑒𝑖𝑡ℎ𝑒𝑟 𝐴 𝑛𝑜𝑟 𝐵 𝐵𝑜𝑡ℎ 𝐴 𝑎𝑛𝑑 𝐵3 + 𝑥2  𝑆𝑖𝑛𝑥