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High School Mathematics - 2
14.3 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 qp => q
TTT
TFF
FTT
FFT

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 qp <=> q
TTT
TFF
FTF
FFT

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.


Directions: Answer the following.
Q 1: Water is dry => Snow is hot. Write T or F.
T
F

Q 2: Construct truth table for (p=>q) ^ (q=>p).
Answer:

Q 3: Construct truth table for q=>[(~p) v q].
Answer:

Q 4: Construct truth table for [(~p) ^ q] => (p v q).
Answer:

Q 5: Let p: I will pass; q: Exam is easy, translate into symbolic form, If the exam is easy, then i will pass.
p=>q
q=>p
p<=>q

Q 6: Let p: I will pass; q: Exam is easy, translate into symbolic form, If I pass, then the exam is easy.
p<=>q
p=>q
q=>p

Q 7: Let p: I will pass; q: Exam is easy, translate into symbolic form, The exam is easy if and only if i pass.
p=>q
p<=>p
q<=>p

Q 8: Let p: I will pass; q: Exam is easy, translate into symbolic form, If the exam is not easy, then i will not pass.
~p=>~q
~q=>~q
~q=>~p

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