Choose the correct answer below.
OA. A true biconditional is "√x 2x if and only if 0x." Both of
these conditionals are true because the graph of y=√x is above the graph of y=x for 0≤x≤ 1 and not for x>1. Because the square root of a negative number is
not a real number, the case of x<0 does not need to be considered.
OB. A true biconditional is "x2 0." One of the implied conditionals is "If x2 0." The other is "If x>0, then x2 conditionals are true because the graph of y=x2 is below the graph of y=x3 for all positive real numbers x and not for any other values of x.
OC. A true biconditional is "A whole number is divisible by 3 if and only if it is divisible by 6." One of the implied conditionals is "If a whole number is divisible by 3, then it
is divisible by 6." The other is "If a whole number is divisible by 6, then it is divisible by 3." Both of these conditionals are true because of the properties of divisibility
and the fact that 6 is a multiple of 3.
OD. A true biconditional is "A whole number is even if and only if it is divisible by 2." One of the implied conditionals is "If a whole number is even, then it is divisible
by 2." The other is "If a whole number is divisible by 2, then it is even." Both of these conditionals are true by the definition of an even number.