Question

A = {a,b, p}, B = {2,3), C = {p,q,r,s} then n|(AUC) x B] is
(1) 8
(2) 20
(3) 12
(4)16​

Answer 1

Answer:

16 is the answer i hope this answer may help you

Answer 2

We need to recall the following definitions for a set.

• The union of two sets $A$ and $B$ is the set of elements that are in $A$, in $B$, or in both $A$ and $B$ .
• If $A$ and $B$ are the two non-empty sets, then the cartesian product $A\times B$ is a set of all ordered pairs $(a,b)$ such that $a\in A$ and $b\in B$.
• The cardinality of a set is the number of elements it contains.

Given:

$A=\{a,b,p\}$ , $B=\{2,3\}$ , $C=\{p,q,r,s\}$

From the definitions of the union and cartesian product of two sets, we get

$(A\cup C)\times B=\{a,b,p,q,r,s\}\times \{2,3\}$

$(A\cup C)\times B=\{(a,2),(b,2),(p,2),(q,2),(r,2),(s,2),(a,3),(b,3),(p,3),(q,3),(r,3),(s,3)\}$

From the definition of cardinality, we get

$n[(A\cup C)\times B]=12$

Hence, the correct option is (3) $12$ .