Question

PLEASE HELP!

Answer 1

Raj's conjecture is valid i.e an even number times an even or odd number will always be even.

Even numbers are number that can be divided by 2 without leaving a remainder. Examples are: 4, 6, 8, 20, 50 etc. While odd numbers can not be divided evenly by 2. Examples are: 7, 11, 17, etc

Thus, the conjecture can be proved as follows:

i. Even number times an even number

• 4 x 12 = 48
• 6 x 8 = 48
• 2 x 10 = 20
• 12 x 16 = 192

Thus, an even number multiplied by an even number would give an even number.

ii. Even number times an odd number

• 4 x 11 = 44
• 6 x 5 = 30
• 2 x 7 = 14
• 8 x 17 = 136
• Thus, an even number multiplied by an odd number would always give an even number.

Therefore, Raj's conjecture is valid.

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