Logical connectives– Conjunction- p ⋀ q Any two propositions can be combined by the word “and” to form a compound proposition called the conjunction of the original propositions. Symbolically,
p∧q
Read “p and q,” denotes the conjunction of p and q. Since p ∧q is a proposition it has a truth value, and this truth
Value depends only on the truth values of p and q.
Note- If p and q are true, then p ∧q is true; otherwise p ∧q is false.
2. Disjunction, p ∨q
Any two propositions can be combined by the word “or” to form a compound proposition called the disjunction of the original propositions. Symbolically,
p∨q
Read “p or q,” denotes the disjunction of p and q. The truth value of p ∨q depends only on the truth values of p
And q as follows-
If p and q are false, then p ∨q is false; otherwise p ∨q is true
Negation
Given any proposition p, another proposition, called the negation of p, can be formed by writing “It is not true that . . .” or “It is false that . . .” before p or, if possible, by inserting in p the word “not.” Symbolically, the negation of p, read “not p,” is denoted by
￢p
The truth value of ￢p depends on the truth value of p as follows-
If p is true, then ￢p is false; and if p is false, then ￢p is true
Basic logical operations of Logical connectives-
Conjunction- p ⋀ q
Any two propositions can be combined by the word “and” to form a compound proposition called the conjunctionof the original propositions. Symbolically,
p∧q
Read “p and q,” denotes the conjunction of p and q. Since p ∧q is a proposition it has a truth value, and this truth
Value depends only on the truth values of p and q.
Note- If p and q are true, then p ∧q is true; otherwise p ∧q is false.
2. Disjunction, p ∨q
Any two propositions can be combined by the word “or” to form a compound proposition called the disjunctionof the original propositions. Symbolically,
p∨q
Read “p or q,” denotes the disjunction of p and q. The truth value of p ∨q depends only on the truth values of p
And q as follows-
If p and q are false, then p ∨q is false; otherwise p ∨q is true
Negation-
Given any proposition p, another proposition, called the negation of p, can be formed by writing “It is not true that . . .” or “It is false that . . .” before p or, if possible, by inserting in p the word “not.” Symbolically, the negation of p, read “not p,” is denoted by
￢p
The truth value of ￢p depends on the truth value of p as follows-If p is true, then ￢p is false; and if p is false, then ￢p is true