Question

“If natural numbers are whole numbers, then rational numbers are integers” or “If rational numbers are integers, then natural numbers are whole numbers” is-
A. a tautology
B. a contradiction
C. a contingency
D. not a statement

Answer 1

Hint: We know that combination of two statements is true when both the statements are false. Here both the given statements are false.

Complete step by step answer:

We are given two statement-
 “If natural numbers are whole numbers, then rational numbers are integers” or
 “If rational numbers are integers, then natural numbers are whole numbers”.
Let the first statement be p and the second statement be q then we know that both statements are false
Then, the truth table will be-

p	q	p$ \Leftrightarrow $ q
F	F	T

Since the combination of two false statements is True. It is a tautology as it is a statement that is true for all truth values of its components.
In tautology, it does not matter whether the truth values are true or false. It is always true and hence also called logically true or logically valid. The contradiction is just the opposite of Tautology.
A contradiction is a proposition that is always false for all truth values. The contradiction is also called a fallacy or logically false statement. A contingency is a statement that is neither a tautology nor a contradiction as it contains both true and false in it.
Hence, the correct answer is A.
Note: The question is a statement as the statement is a sentence which is either true or false but not both.
Statements are of two types-atomic statements that cannot be further broken and molecular statements that can be further broken.