**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