Explanation

The given set:

Z = {0, ±1, ±2, ±3, ±4, ...}

This set includes all integers, both positive and negative, as well as zero.

Explanation

A rational number is defined as a number that can be expressed as the ratio of two integers, i.e., a/b, where a and b are integers and b ≠ 0.

Every rational number can be written in the form of a fraction, where the numerator and denominator are integers.

Example: 3/4, 22/7, 1/2, etc.

Explanation

Given:

√x is an integer

This means that x is a perfect square, since the square root of x is an integer.

Examples: x = 1, 4, 9, 16, 25, ...

Explanation

To check if a number is exactly divisible by 4, we can check if the last two digits form a number that is divisible by 4.

2000: Last two digits are 00, which is divisible by 4.

Since 2000 ends in 00, it is exactly divisible by 4.

Explanation

Given:

A = {2, 4, 6, 10}

The symbol ∈ means "is an element of".

Since 4 is an element of set A, the correct representation is:

4 ∈ A

Explanation

"Talked" is the verb in the sentence because:

It is the action word (what they did).

It functions as the past tense of "talk."

Explanation

"And" is the conjunction in the sentence because:

It connects similar elements (bananas, oranges, grapes).

It joins words of the same grammatical type (nouns).

Explanation

"Zaira" is the subject of the sentence because:

It is the doer of the action (the one who loves).

It answers the question: "Who loves raw mangoes?"

Explanation

"I stayed home." is a simple sentence because:

It has one independent clause (subject: I, verb: stayed).

It expresses a complete thought without extra clauses.

Explanation

"Is he going to market?" is grammatically correct because:

It uses the correct helping verb "is" (for present continuous tense).

The structure follows "Is + subject + verb-ing?"