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# The universal set $$U$$ consists of all integers subsets of $$U$$ are defined as...

### Question

The universal set $$U$$ consists of all integers subsets of $$U$$ are defined as:
$$A = {y: y \leq 3}$$
$$B = {y: −5 < y < 12}$$
$$C = {y: −2 \leq y < 5}$$
$$A{\cap}(B{\cup}C)'$$ is

### Options

A) $$\{y < -4\}$$

B) $$\emptyset$$

C) $$\{y < 0\}$$

D) $$\{-4{\leq}y{\leq}3\}$$

### Explanation:

$$U = \{...,-3,-2,-1,0,1,2,...\}$$
$$A = \{...,-3,-2,-1,0,1,2\}$$
$$B = \{-4,-3,-2,-1,0,1,...,11\}$$
$$C= \{-2,-1,0,1,2,3,4\}$$
$$(B{\cup}C)=\{...,-5,12,13,...\}$$
$$A{\cap}(B{\cup}C)=\{...,-5\}$$
$$=\{y<-4\}$$

## Dicussion (1)

• $$U = \{...,-3,-2,-1,0,1,2,...\}$$
$$A = \{...,-3,-2,-1,0,1,2\}$$
$$B = \{-4,-3,-2,-1,0,1,...,11\}$$
$$C= \{-2,-1,0,1,2,3,4\}$$
$$(B{\cup}C)=\{...,-5,12,13,...\}$$
$$A{\cap}(B{\cup}C)=\{...,-5\}$$
$$=\{y<-4\}$$