Question

Let A= {1,2} and B= {3,4}.Write A×B. How many subsets will A×B have? List them.​

Answer 1

• A × B = { (1,3) , (1,4) , (2,3) , (2,4) }

• A × B has 16 subsets

Given :

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

To find :

• A × B

• The number of subsets of A × B

Concept :

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

The given sets are

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

Step 2 of 3 :

Find A × B

Here it is given that

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

Thus we get

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

∴ A × B = { (1,3) , (1,4) , (2,3) , (2,4) }

Step 3 of 3 :

Find number of subsets of A × B

We have

A × B = { (1,3) , (1,4) , (2,3) , (2,4) }

Since A × B has 4 elements

So the number of subsets of A × B

$\sf = {2}^{4}$

$\sf = 16$

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