**Example 1**:

Form a compound statement by combining two given statements
using the word ‘and’.

**(a)**3 × 12 = 36

7 × 5 = 35

**(b)**5 is a prime number.

5 is an odd number.

**(c)**Rectangles have 4 sides.

Rectangles have 4 vertices.

*Solution:***(a)**3 × 12 = 36 and 7 × 5 = 35

**(b)**5 is a prime number and an odd number.

**(c)**Rectangles have 4 sides and 4 vertices.

**Example 2**:

Form a compound statement by combining two given statements
using the word ‘or’.

**(a)**16 is a perfect square. 16 is an even number.

**(b)**4 > 3. -5 < -1

*Solution:***(a)**16 is a perfect square or an even number.

**(b)**4 > 3 or -5 < -1.

**Example 3**:

Determine whether each of the following statements is true
or false.

**(a)**3 × (-4) = -12 and 13 + 6 = 19

**(b)**100 × 0.7 = 70 and 12 + (-30) = 18

*Solution:*
When two statements are combined using ‘

**and**’, a**true**compound statement is obtained only if**both**statements are**true**.
If

**one or both**statements are**false**, then the compound statement is**false**.**(a)**Both the statements ‘3 × (-4) = -12’ and ‘13 + 6 = 19’ are true. Therefore, the statement ‘3 × (-4) = -12 and 13 + 6 = 19’ is

**true**.

**(b)**The statement ‘12 + (-30) = 18’ is false. Therefore, the statement ‘100 × 0.7 = 70 and 12 + (-30) = 18’ is

**false**.

**Example 4**:

Determine whether each of the following statements is true
or false.

**(a)**

*m*+

*m*=

*m*

^{2}or

*p*×

*p*×

*p*=

*p*

^{-}^{3}

**(b)**$\sqrt[3]{64}=-4\text{or}\sqrt[3]{-27}=-3$

*Solution:*
When two statements are combined using ‘

If **or**’, a**false**compound statement is obtained only if**both**statements are**false**.**one or both**statements are

**true**, then the compound statement is

**true**.

**(a)**Both the statements ‘

*m*+

*m*=

*m*

^{2}’ and ‘

*p*×

*p*×

*p*=

*p*

^{-}^{3}’ are false. Therefore the statement

*m*+

*m*=

*m*

^{2}or

*p*×

*p*×

*p*=

*p*

^{-}^{3}is

**false**.

**(b)**The statement $\text{'}\sqrt[3]{-27}=-3\text{'}$is true. Therefore, the statement $\text{'}\sqrt[3]{64}=-4\text{or}\sqrt[3]{-27}=-3\text{'}$is

**true**.