Explanation

The given set:

{x|x ∈ N, 1 ≤ x < 4}

Can be read as:

The set of all natural numbers x such that 1 ≤ x < 4

This includes the numbers 1, 2, and 3, but excludes 4.

Explanation

The correct definition of rational numbers is:

The set of all numbers of the form p/q where p and q are integers and q ≠ 0.

This is because rational numbers are defined as the ratio of two integers, with the denominator (q) being non-zero.

Explanation

The conjugate of a complex number or expression is obtained by changing the sign of the imaginary part or irrational part.

The given expression is -3 - √5, so its conjugate is -3 + √5.

Explanation

The sum of 21 and 24 is 45.

The HCF of 21 and 24 is 3. Thus, 21 and 24 satisfy both conditions.

Explanation

The given expression:

(x/x ∈ A and x ∈/ B)

Can be read as:

x is an element of A and x is not an element of B

This represents the set difference between A and B, which is denoted as:

A B or A - B

The correct answer is: AB

Explanation

Given equations:

a + b = 10 ... (1)

3a + 2b = 40 ... (2)

We need to find 3a + b.

Multiply equation (1) by 2:

2a + 2b = 20 ... (3)

Subtract equation (3) from equation (2):

(3a + 2b) - (2a + 2b) = 40 - 20

a = 20

Now, find b:

a + b = 10

20 + b = 10

b = -10

Calculate 3a + b:

3a + b = 3(20) + (-10)

= 60 - 10

= 50

Explanation

To find the profit percentage:

Profit = Sale Price - Cost Price

= 750 - 570

= 180

Profit Percentage = (Profit / Cost Price) × 100

= (180 / 570) × 100

= 0.31579 × 100

≈ 31.578%

Explanation

The cubed value of a fraction (where the numerator and denominator are both less than 1) is always smaller than the original fraction.

This happens because cubing a fraction between 0 and 1 makes it even smaller.

Explanation

The point of intersection of the angle bisectors of a triangle is called the incenter.

The incenter is equidistant from all three sides of the triangle, as it is the center of the incircle (the circle inscribed within the triangle).

Explanation

1 is not a prime number because it has only one factor (1).

It’s also not composite because composite numbers have more than two factors.