Question

The truth-value of “\[10 + 2 = 12{\text{ and }}10 \times 2 = 20\]” is
A. T
B. F
C. T or F
D. T and F

Answer 1

Hint: First we first see that the statements are connected by ‘AND’. Then the truth-value would be false if one of the statements evaluate to false, we check for both the statements to find the required value.

Complete step by step answer:

We need to evaluate the truth-value of “ \[10 + 2 = 12{\text{ and }}10 \times 2 = 20\] ”.
We know that the statements are connected by ‘AND’.
We also know that both of the statements need to be true for the “AND” statement is true.
This implies that the truth-value would be false if one of the statements evaluated is false.
Since we have that the truth-value of \[10 + 2 = 12\] is true as when 10 is added with 2 is 12 and the truth-value of \[10 \times 2 = 20\] is also true as when 2 multiply 10 is 20.
As we have both the statements are true, the truth-value of the sentence is T.
Hence, option A is correct.
Note: Students must know that the property of a statement of being either true or false. All statements have truth-value true if both of the statements need to be true for the “AND” statement is true, else false. If we are given an OR condition then the statement will become true if any one of the statements given is true.