Let X = nN : 1 n50.

Question

Let $X = \{n\in\mathbb{N} : 1\leq n\leq50\}$. If $A = \{n\in X : n 	ext{ is a multiple of } 2\}$ and $B=\{n\in X : n 	ext{ is a multiple of } 7\}$, then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is:

Answer: 29

Accepted Answer

$n(A) = 25$ (multiples of 2 up to 50). $n(B)=7$ (multiples of 7: $7,14,\ldots,49$). $n(A\cap B)$ = multiples of 14 up to 50 $=3$ ($14,28,42$).

The smallest subset containing both is $A\cup B$:
$$n(A\cup B) = 25+7-3 = 29$$

Solutions · 1