Question

True Or False

1. If nn is odd and the square root of nn is a natural number then the square root of nn is odd.

2. The square of any even integer is even

3. The substraction of 2 rational numbers is rational.

4. If nn is an odd integer, then n2+nn2+n is even.

5. If a divides b and a divides c then a divides bc.

6. For all real numbers a and b, if a^3=b^3 then a=b.

Answer 1

2. The square of any even integer is even

true , square of an even number is always even

3. The substraction of 2 rational numbers is rational.

True a rational number is any number that can be represented as a fraction , so if we sustract 1 rational from another , we still get a rational number

5. If a divides b and a divides c then a divides bc.

Suppose first that a|b. Then there is an integer r such that b = ar. Then bc = arc =
a(rc). Since rc is an integer, a|bc. A similar argument works if a|c

6.
Let us try solving it step by step.
a^3=b^3
=> a^3 - b^3 =0
=> (a-b) * (a^2 + b^2 + a*b)= 0

Now solving this we get either a=b or
from the quadratic a=b*(1 + sqrt(-3))/2 or
a=b*(1 - sqrt(-3))/2
Hence, the answer is no.

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