Question

If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ) = Φ.

Answer 1

Answer:

Proved

Step-by-step explanation:

It is proved

LHS=RHS

Answer 2

If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ) = Φ is proved

Given :

A = {1, 2}, B = {3, 4}

To prove :

A × (B ∩ Φ) = Φ

Solution :

Step 1 of 3 :

Define 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

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

Step 2 of 3 :

Find B ∩ Φ

B = {3, 4}

We know that Φ is empty set containing no element

Thus we have

B ∩ Φ = Φ

Step 3 of 3 :

Prove the expression

LHS

= A × (B ∩ Φ)

= A × Φ

= Φ

= RHS

Hence proved

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