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# What are Logical connectives?

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,

pq

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,

pq

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