If A = {1, 2} and B = {3, 4}, Determine the number of relations from A and B:

Option b: 16. Solution: We are given sets: A = {1, 2} implies n(A) = 2 B = {3, 4} implies n(B) = 2 The number of elements in the Cartesian product A x B is: n(A x B) = n(A) x n(B) = 2 x 2 = 4 A relation from A to B is defined as any subset of A x B. Since a set with k elements has 2^k subsets, the total number of relations (which are subsets of A x B) is: text{Number of relations} = 2^{n(A x B)} = 2^4 = 16 Hence, Option B is the correct answer.

If $A = \{1, 2\}$ and $B = \{3, 4\}$, Determine the number of relations from $A$ and $B$:

The correct answer is Option b: 16. We are given sets: $$A = \{1, 2\} \implies n(A) = 2$$ $$B = \{3, 4\} \implies n(B) = 2$$ The number of elements in the Cartesian product $A \times B$ is: $$n(A \times B) = n(A) \times n(B) = 2 \times 2 = 4$$ A relation from $A$ to $B$ is defined as any subset of $A \times B$. Since a set with $k$ elements has $2^k$ subsets, the total number of relations (which are subsets of $A \times B$) is: $$\text{Number of relations} = 2^{n(A \times B)} = 2^4 = 16$$ Hence, **Option B** is the correct answer.

Set, Relations and FunctionsPYQ Nov. 18Question 1941 of 217

All Questions

If $\displaystyle A = \{1, 2\}$ and $\displaystyle B = \{3, 4\}$ , Determine the number of relations from $\displaystyle A$ and $\displaystyle B$ :

Options

B16

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 16

All Options:

Detailed Solution & Explanation

We are given sets:

A = \{1, 2\} \implies n(A) = 2

B = \{3, 4\} \implies n(B) = 2

The number of elements in the Cartesian product

\displaystyle A \times B

is:

n(A \times B) = n(A) \times n(B) = 2 \times 2 = 4

A relation from

\displaystyle A

\displaystyle B

is defined as any subset of

\displaystyle A \times B

.
Since a set with

\displaystyle k

elements has

\displaystyle 2^k

subsets, the total number of relations (which are subsets of

\displaystyle A \times B

) is:

\text{Number of relations} = 2^{n(A \times B)} = 2^4 = 16

Hence, **Option B** is the correct answer.

Ready to Master Set, Relations and Functions?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If A={1,2}\displaystyle A = \{1, 2\}A={1,2} and B={3,4}\displaystyle B = \{3, 4\}B={3,4}, Determine the number of relations from A\displaystyle AA and B\displaystyle BB: