For the statement below tell whether or not the statement is true. If the statem

Question

For the statement below tell whether or not the statement is true. If the statement is true, write a proof that demonstrates that fact. If the statement is false, provide a counter example to disprove it. a) if a is any odd integer, then a^2 + a is even. b) The quotient of any two rational numbers is a rational number.

Explanation / Answer

a. True a is odd => a+1 is even a^2 + a = a ( a+1) = odd* even = even B. FALSE x =p/q where q not equal to 0 y = m/n where n is not equal to 0 x/y = pn/mq Since m can be zero , the denominator can be zero. therefore , x/y is not necessarily a rational number

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