Given A = (2, 3), B = (4, 5), C = (5, 6) then A x (B cap C) is

Option a: (2,5), (3,5). Solution: We are given three sets: A = {2, 3} B = {4, 5} C = {5, 6} First, let us find the intersection of B and C (common elements): B cap C = {5} Now, we compute the Cartesian product A x (B cap C): A x (B cap C) = {2, 3} x {5} The Cartesian product is the set of all ordered pairs (a, x) where a in A and x in B cap C: A x (B cap C) = {(2, 5), (3, 5)} Hence, Option A is the correct answer.

Given $A = (2, 3)$, $B = (4, 5)$, $C = (5, 6)$ then $A \times (B \cap C)$ is

The correct answer is Option a: $(2,5), (3,5)$. We are given three sets: $A = \{2, 3\}$ $B = \{4, 5\}$ $C = \{5, 6\}$ First, let us find the intersection of $B$ and $C$ (common elements): $$B \cap C = \{5\}$$ Now, we compute the Cartesian product $A \times (B \cap C)$: $$A \times (B \cap C) = \{2, 3\} \times \{5\}$$ The Cartesian product is the set of all ordered pairs $(a, x)$ where $a \in A$ and $x \in B \cap C$: $$A \times (B \cap C) = \{(2, 5), (3, 5)\}$$ Hence, **Option A** is the correct answer.

Set, Relations and FunctionsPYQ June 22Question 1896 of 217

All Questions

Given $\displaystyle A = (2, 3)$ , $\displaystyle B = (4, 5)$ , $\displaystyle C = (5, 6)$ then $\displaystyle A \times (B \cap C)$ is

Options

\displaystyle (2,5), (3,5)

\displaystyle (5,2), (5,3)

\displaystyle (2,3), (5,5)

DNone of these

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Correct Answer

✅ Option a — $\displaystyle (2,5), (3,5)$

All Options:

A $\displaystyle (2,5), (3,5)$
B $\displaystyle (5,2), (5,3)$
C $\displaystyle (2,3), (5,5)$
DNone of these

Detailed Solution & Explanation

We are given three sets:

\displaystyle A = \{2, 3\}

\displaystyle B = \{4, 5\}

\displaystyle C = \{5, 6\}

First, let us find the intersection of

\displaystyle B

and

\displaystyle C

(common elements):

B \cap C = \{5\}

Now, we compute the Cartesian product

\displaystyle A \times (B \cap C)

A \times (B \cap C) = \{2, 3\} \times \{5\}

The Cartesian product is the set of all ordered pairs

\displaystyle (a, x)

where

\displaystyle a \in A

and

\displaystyle x \in B \cap C

A \times (B \cap C) = \{(2, 5), (3, 5)\}

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

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Given A=(2,3)\displaystyle A = (2, 3)A=(2,3), B=(4,5)\displaystyle B = (4, 5)B=(4,5), C=(5,6)\displaystyle C = (5, 6)C=(5,6) then A×(B∩C)\displaystyle A \times (B \cap C)A×(B∩C) is