Chapter 3 - Logic - 3.5 Equivalent Statements and Variations of Conditional Statements - Exercise Set 3.5 - Page 171: 44

The converse of conditional statements is obtained by reverse the conditional statements. The inverse of conditional statements is obtained by negating them individually to the conditional statements.

Consider the conditional statement that is written below: “If Ram is ill, then he is vomiting”. Take \[p\]statement as“Ram is ill” and \[q\] statement as “Ram is vomiting”. Then, write symbol notation of the conditional statement: \[p\to q\] It signifies that it is a conditional statement if Ram is ill then he must be vomiting. Then write, the provided statement into a converse statement as the converse statement is the reverse of the statement. So, the converse statement is as follows: If Ram is vomiting, then he is ill. It’s symbolic statement, \[q\to p\] It signifies that it is basically a conditional statement, if Ram is vomiting, then he is ill. The truth value of a conditional statement may or may not be changed if first part and the second part of a conditional statement are reversed then that statement \[q\to p\] is known as the converse of a conditional statement, which is\[p\to q\]. Further, write the provided statement into an inverse statement as the inverse statement is the negation of the statement. So, the inverse statement is as follows: If Ram is not ill, then he is not vomiting. It’s symbolic statement, \[\sim p\to \sim q\] It signifies that it is a basically conditional statement if Ram is not ill then he is not vomiting. The truth value of a conditional statement may or may not be changed if first part and the second part of a conditional statement are negated them individually, then that statement \[\sim p\to \sim q\] is known as the converse of a conditional statement, which is\[p\to q\]. Here, a truth table is listed below to show that their truth values need not be necessarily true: \[p\] \[q\] \[p\to q\] \[q\to p\] \[\sim p\to \sim q\] T T T F F Example: Take a conditional statement that is written below: “If Ram is ill then he is vomiting”. Then write its converse statement, If Ram is vomiting, then he is ill. Further, write its inverse statement, If Ram is not ill, then he is not vomiting.