Page 244 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

The first two sentences are not declarative sentences and not propositions.
The last two sentences are neither true nor false and so they are not propositions.
A proposition variable is represented by one of the letters p, q, r, s, ...
If a proposition is true then its truth value is denoted by T and if the proposition is false then its truth value is denoted by F. Sometimes 1 and 0 are used instead of T and F respectfully.
NEGATION
Ipad is an Apple product. Ipad is not an Apple product.
Or
It is false that Ipad is an Apple product.
Or
It is not the case that Ipad is an Apple product.
If p is a proposition then the negation of p is denoted by np and is read as ‘not p?
The truth value of p, np, is the opposite of the truth value of p.
Let p: And q:
CONJUNCTION
Breadfruit is a jackfruit family. Breadfruit is eaten by West Indians.
Then p^q: Breadfruit is a jackfruit family and it is eaten by West Indians.
The conjunction of p and q is denoted as p^q.
The conjunction of p and q is denoted by p^q. It is the propoitiob ‘p and q’. The conjunction p6q is true when both p and q are true, and it is false otherwise.
p
q
p^q
T
T
T
T
F
F
F
T
F
F
F
F
Let p: Then np:
This is the truth table for p^q, the conjunction of two propositions. Disjunction
DISJUNCTION
Let p: Neil Armstrong was an American astronaut. And q: Neil Armstrong was a Russian astronaut.
Then pvq: Neil Armstrong was an American astronaut or a Russian astronaut.
The disjunction of p and q is denoted as pvq.
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
np
T
F
F
T
This is the truth table for np.
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