Question

Assertion: `3/4` is a rational number lying between 2 rational numbers `1/2` and `7/8`.

Reason: A number lying between a and b is `1/2` (ab).

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is true but R is false.

Explanation:

Assertion (A):

• `3/4` is a rational number lying between two rational numbers `1/2` and `7/8`.
• `1/2 = 0.5, 3/4 = 0.75, 7/8 = 0.875`.
• Clearly, 0.5 < 0.75 < 0.875.

Reason (R):

A number lying between a and b is `1/2` (ab).

• This is false.
• The correct formula for a number between a and b is their arithmetic mean: `(a + b)/2`
• Multiplying a and b and halving is not a general method.