Page 245 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

The disjunction of p and q is denoted by pvq. It is the proposition ‘p or q’. the disjunction pvq are false and it is true otherwise.
p
q
p→q
T
T
T
T
F
T
F
T
T
F
F
T
p
q
pvq
T
T
T
T
F
T
F
T
T
F
F
F
This is the truth table for pvq, the disjunction of two propositions.
This is the truth table for p → q the conditional statement or implication.
LOGICAL EQUIVALENCES
The compound propositions p and s are called logically equivalent if the last column of their truth tables have the same truth values in all possible cases. The notation r 􏰀 s denotes that r and s are logically equivalent.
EXAMPLE 16
Let p: Sherone Simpson is a Jamaican track and field athlete.
nd q: Don Quarrie is a former Jamaican track and field athlete.
(a) Express each of the following compound propositions as an English sentence.
(i) n(p^q) (ii) npv nq.
(b) Do the two English sentences mean the same thing?
(c) Construct truth tables to show that n (p^q) 􏰀 npvnq.
Let p: And q:
CONDITIONAL STATEMENT
I am prime minister.
I will remove VAT from all items.
Then p → q: If I am prime minister then I will remove VAT from all items.
A conditional statement asserts that q is true an the condition that p holds and it is denoted as
p → q.
A conditional statement is also called an implication.
The conditional statement p → q is the proposition ‘if p then q? In the conditional statement p →q, p is called the hypothesis (or antecedent or premise) and q is called the conclusion (or consequence). The implication p →q is false when p is true and q is false, and it is true other wise.
239
(a) (i) p^q: n(p^q):
Sheron Simpson is a Jamaican track and field athlete and Don Quarrie is a former Jamaican track and field athlete.
It is false that Sheron Simpson is a Jamaican track and field athlete and Don Quarrie is a former Jamaican track and field athlete.