Question

Given below are two statements:
p: 25 is a multiple of 5.
q: 25 is a multiple of 8.
write the compound statements connecting these two statements with "and" and "or". In both cases check the validity of the compound statement.

Answer 1

Hint: In this problem, we first create the compound statement by using the connectives given in the problem statement. Then, we will verify the logical equivalence of the final compound statement in each case. In this way we can easily solve the problem.

Complete step-by-step answer:
One of the most important branches of mathematics is mathematical reasoning. It includes the analysis statement by using truth tables and results. A statement for a proposition is an assertive sentence which is either true or false but not both. The phrases or words which connect simple statements are called logical connectives. This includes and, or, if then, not etc. In our question we have to combine two statements P and Q by using "and" and "or".
By using the connective "and", we get
A: 25 is a multiple of 5 and 8.
By using the connective "or", we get
B: 25 is a multiple of 5 or 8.
Now, for checking the logical equivalence of both the statements:
Statement (A) is false because 25 is a multiple of 5 but not 8.
Statement (B) is true because 25 is a multiple of 5.
Note: The key step for solving this problem is the knowledge of mathematical reasoning and the usage of connectives for two statements. Truth and falsity of a statement needs to be critically analysed by the student.