If B subseteq A, A cap B^prime=1,4,5 and A cup B=1,2,3,4,5,6 , then find set B .

Question

Answer 1

## Step 1: Understand the Given Sets### We are given that

,

, and

. Here,

represents the complement of

with respect to

.## Step 2: Determine Set

### Since

, these elements are in

but not in

. Therefore,

must include these elements. Additionally, since

, all elements of

are also in

.## Step 3: Use Union Information### The union

implies that all elements of both sets

and

are included in this set. Thus,

must contain all elements from

and any additional elements needed to satisfy the union.## Step 4: Find Set

### Since

and

, the elements

and

cannot be in

. The remaining elements

and

must be in

to satisfy

.

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