Question

If A= {1, 2, 4}, B={2, 4, 5}, C={2, 5}, find (A-B) x (B-C).

Answer 1

The answer to your question is given above in the pic. I hope that it helps you!!!

Answer 2

(A - B) × (B - C) = { (1,4) }

Given :

A = {1, 2, 4} , B = {2, 4, 5} , C = {2, 5}

To find :

The set (A - B) × (B - C)

Concept :

Difference of two set :

For two given set A and B , the difference of two sets is denoted by A - B and defined as

A - B = { x : x ∈ A : x ∉ B }

Cartesian Product :

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

Solution :

Step 1 of 3 :

Write down the given sets

Here the given sets are

A = {1, 2, 4} , B = {2, 4, 5} , C = {2, 5}

Step 2 of 3 :

Find (A - B) and (B - C)

A - B

= { x : x ∈ A : x ∉ B }

= {1}

B - C

= { x : x ∈ B : x ∉ C }

= {4}

Step 3 of 3 :

Find the set (A - B) × (B - C)

(A - B) × (B - C)

= { (x, y) : x ∈ (A - B) and y ∈ (B - C) }

= { (1,4) }

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