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### High School Mathematics - 214.3 Conditional Statements

We frequently come across statements like:
"If p then q" are called conditional statements and denoted as p=>q and read as p implies q.
Truth table for a conditional
 p q p => q T T T T F F F T T F F T

A statement of the form "p if and only if q" are called biconditional statements and are denoted by p<=>q.
Biconditional Statement
Truth table for a biconditional
 p q p <=> q T T T T F F F T F F F T

Regarding the truth values of p=>q and p<=>q, we have

1. The conditional p=>q is false only if p is true and q is false. Accordingly, if p is false, then p=>q is true regardless of the truth value of q.
2. The biconditional p<=>q is true whenever p and q have the same truth values, otherwise it is false.

 Q 1: Let p: I will pass; q: Exam is easy, translate into symbolic form, If the exam is easy, then i will not pass.p<=>qq=>~pp=>q Q 2: Let p: I will pass; q: Exam is easy, translate into symbolic form, If I don't pass, then the exam is not easy.~p=>~qp=>~q~p=>q Q 3: Let p: I will pass; q: Exam is easy, translate into symbolic form, If the exam is not easy, then i will not pass.~q=>~p~q=>~q~p=>~q Q 4: Construct truth table for q=>[(~p) v q].Answer: Q 5: Construct truth table for [(~p) ^ q] => (p v q).Answer: Q 6: Let p: I will pass; q: Exam is easy, translate into symbolic form, The exam is easy if and only if i pass.q<=>pp=>qp<=>p Q 7: Let p: I will pass; q: Exam is easy, translate into symbolic form, If I pass, then the exam is easy.q=>pp=>qp<=>q Q 8: Construct truth table for (p=>q) ^ (q=>p).Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!