Suppose that Qx is the statement x 2 2x What are the truth

Suppose that Q(x) is the statement “x + 2 = 2x.” What are the truth values of the following statements? Assume x is representing all real numbers. xQ(x)____________________ xQ(x)____________________

Solution

a) xQ(x) is False since 1+2 is not equal to 2*1 and this statement requires Q(x) to be true for all x in the domain of real numbers

b) xQ(x) is True since 2+2 = 2*2 and this statement requires Q(x) to be true for some x in the domain of real numbers