If A = (1, 2, 3, 4, 5, 6, 7) and B = (2, 4, 6, 8). Cardinal number of A - B is:

Option a: 4. Solution: We are given two sets: A = {1, 2, 3, 4, 5, 6, 7} B = {2, 4, 6, 8} The difference set A - B is defined as the set containing elements that belong to A but do not belong to B: A - B = {x mid x in A text{ and } x notin B} Let us identify the common elements of A and B: A cap B = {2, 4, 6} Subtracting these common elements from A: A - B = {1, 2, 3, 4, 5, 6, 7} - {2, 4, 6} = {1, 3, 5, 7} The cardinal number (or cardinality) of a set is the number of elements in it. Let n(A - B) represent the cardinal number of A - B: n(A - B) = 4 Hence, Option A is the correct answer.

If $A = (1, 2, 3, 4, 5, 6, 7)$ and $B = (2, 4, 6, 8)$. Cardinal number of $A - B$ is:

The correct answer is Option a: 4. We are given two sets: $A = \{1, 2, 3, 4, 5, 6, 7\}$ $B = \{2, 4, 6, 8\}$ The difference set $A - B$ is defined as the set containing elements that belong to $A$ but do not belong to $B$: $$A - B = \{x \mid x \in A \text{ and } x \notin B\}$$ Let us identify the common elements of $A$ and $B$: $$A \cap B = \{2, 4, 6\}$$ Subtracting these common elements from $A$: $$A - B = \{1, 2, 3, 4, 5, 6, 7\} - \{2, 4, 6\} = \{1, 3, 5, 7\}$$ The cardinal number (or cardinality) of a set is the number of elements in it. Let $n(A - B)$ represent the cardinal number of $A - B$: $$n(A - B) = 4$$ Hence, **Option A** is the correct answer.

Set, Relations and FunctionsPYQ Nov. 18Question 1886 of 217

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If $\displaystyle A = (1, 2, 3, 4, 5, 6, 7)$ and $\displaystyle B = (2, 4, 6, 8)$ . Cardinal number of $\displaystyle A - B$ is:

Options

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Correct Answer

✅ Option a — 4

All Options:

Detailed Solution & Explanation

We are given two sets:

\displaystyle A = \{1, 2, 3, 4, 5, 6, 7\}

\displaystyle B = \{2, 4, 6, 8\}

The difference set

\displaystyle A - B

is defined as the set containing elements that belong to

\displaystyle A

but do not belong to

\displaystyle B

A - B = \{x \mid x \in A \text{ and } x \notin B\}

Let us identify the common elements of

\displaystyle A

and

\displaystyle B

A \cap B = \{2, 4, 6\}

Subtracting these common elements from

\displaystyle A

A - B = \{1, 2, 3, 4, 5, 6, 7\} - \{2, 4, 6\} = \{1, 3, 5, 7\}

The cardinal number (or cardinality) of a set is the number of elements in it. Let

\displaystyle n(A - B)

represent the cardinal number of

\displaystyle A - B

n(A - B) = 4

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

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If A=(1,2,3,4,5,6,7)\displaystyle A = (1, 2, 3, 4, 5, 6, 7)A=(1,2,3,4,5,6,7) and B=(2,4,6,8)\displaystyle B = (2, 4, 6, 8)B=(2,4,6,8). Cardinal number of A−B\displaystyle A - BA−B is: