Question

Which of the following compound statements is true after writing the component statements of each compound statement?

• A. A line is straight and extends indefinitely in both directions
• B. $0$ is greater than every positive integer and less than every negative integer
• C. All living things have two legs and two eyes
• D. $42$ is divisible by $4$ and $5$

Answer 1

Answer: (A)

A line is straight and extends indefinitely in both directions

Answer 2

(a) The component statements are $p :$ A line is straight. $q :$ A line extends indefinitely in both directions. Both these statements are true. Therefore, the compound statement is true. (b) The component statements are $p: 0$ is greater than every positive integer. $q: 0$ is less than every negative integer. Both statements are false. Therefore, the compound statement is false. (c) The component statements are $p :$ All living things have two legs. $q :$ All living things have two eyes. Both these statements are false. Therefore, the compound statement is false. (d) The component statements are $p : 42$ is divisible by $4$. $q: 42$ is divisible by $5$. Both the statements are false. So compound statement is false.