Question

What is the truth value of the statement \[2 \times 3 = 6\] or $5 + 8 = 10?$
(A) True
(B) False
(C) Neither True nor False
(D) Cannot be determined

Answer 1

Hint: A statement in mathematics is a sentence that expresses a mathematical relation. These mathematical statements can be either true or false. But if we are given more than one statement and we are to find whether the pair of statements are true or false, we use the truth table for this case.

Complete answer:For truth tables, we assign the value $1$ for a true statement and $0$ for a false one.
Now let $A$ and $B$ be two statements and we are to find out the truth value of $A$ or $B$ which is mathematically expressed as the truth value of $A + B$. Now the basic truth table of $A$ or $B$ is given by

A	B	A+ B
T	T	T
T	F	T
F	T	T
F	F	F

where T denotes true value and F denotes the false value.
Now for the given problem, we are to find out the truth value of the statement \[2 \times 3 = 6\] or $5 + 8 = 10$. We all know that $2 \times 3 = 6$ is an absolutely true statement. But the next statement $5 + 8 = 10$ is never true or it is false. Therefore we are to deal with a T or F. According to the truth table, we get value T in this case.
Therefore the required truth value of the statement \[2 \times 3 = 6\] or $5 + 8 = 10$ is T i.e., True.

Note:
Note that, in mathematical logic, the term ‘or’ is used as the mathematical operation $ + $ . There is another case which is ‘and’. For ‘and’, we treat it as the multiplication operation i.e., $ \times $. It is quite evident that the outputs of these different logic gates or simply truth tables are destined to be different. The truth table of ‘or’ is called an ‘Or Gate’ and the truth table of ‘and’ is called the ‘And Gate’.