U = {1, 2, 3, 6, 7, 12, 17, 21, 35, 52, 56},
P = {numbers divisible by 7}, Q = {prime numbers}

List the elements of the set {x : x ∈ P ∩ Q}

Question

U = {1, 2, 3, 6, 7, 12, 17, 21, 35, 52, 56},P = {numbers divisible by 7}, Q = {prime numbers}List the elements of the set {x : x ∈ P ∩ Q}

Philoid · Accepted Answer

U = {1, 2, 3, 6, 7, 12, 17, 21, 35, 52, 56}

Numbers divisible by 7 present in U are: 7, 21, 35, 56.

Prime numbers present in U are : 2, 3, 7, 17.

∴ P = {7, 21, 35, 56}

∴ Q = {2, 3, 7, 17}

∴ P ∩ Q = {7} [elements that are present in both P and Q]

∴ The set {x : x ∈ P ∩ Q} = {7}