If 𝑈 = {1,2,3,4,5,6,7,8,9,10,11,12}, 𝐴 = {2,3,5,6}, 𝐵 = { 1,5,7,8,10,12}, 𝐶 = {8,10,11,12}. 𝐹𝑖𝑛𝑑 𝐴 ∪ 𝐵, 𝐴 ⊕ 𝐵, 𝐵 ∖ 𝐶, |𝑃(𝐴)|

a.

The union of the sets A and B, denoted by $A\cup B,$ is the set that contains those elements that are either in A or in B, or in both.

$A\cup B=\{1,2,3,5,6,7,8,10,12\}$

b.

The symmetric difference of A and B, denoted by A ⊕ B, is the set containing those elements in either A or B, but not in both A and B.

$𝐴 ⊕ 𝐵=\{1,2,3,6,7,8,10,12\}$

c.

The difference of B and C, denoted by $𝐵 ∖ 𝐶$ , is the set containing those elements that are in B but not in C. 

$𝐵 ∖ 𝐶=\{1,5,7\}$

d.

Cardinality denotes the total number of elements in the power set. It is denoted by |P(A)|. The cardinality of a power set for a set of $n$ elements is given by $2^n$

$|𝑃(𝐴)|=2^4=16$