Write in symbolic language determine if the statement is tru

Write in symbolic language, determine if the statement is true or false (with justification) and negate the statement: \"If the product of a rational number x and a non zero real number y is rational, then x is zero or y is rational\". \"Reciprocals of natural numbers are smaller than or equal t one\". Let P and Q be mathematical statements. Then P Q and P Q are logically equivalent.

Solution

a) TRUE, since it must be a zero or y must be rational since product of rational and irrational will be irrational in nature

b) The second statement is TRUE

Since the natural number series will be from (1,2,3,....)

The maximum value of the reciprocal of natural number will be 1/1 = 1

Hence the statement above is CORRECT

c) The statement is FALSE, the truth table for P=>Q will give a 0 when P=1 and Q=0, but PVQ will be 1 this time since one of two is 1

Therefore, the two statements are not logically equivalent