**And**

**If p and q are statements, then the conjunction of p and q is denoted by**

**p ^ q**

**and is read as "p and q".**

**If both p and q are true then p ^ q is true, and otherwise it is false.**

**Or**

**If p and q are statements, then the disjunction of p and q is denoted by**

**p ∨q , and is read as "p or q".**

**If at least one of p and q is true, then p ∨q is true. If both p and q are**

**false then p ∨ q is false.**

**Thus the statement**

**1 = 1 or 1 = 2 is true.**

**IFF**

If p and q are statements, then the statement

p <=> q

is read as "p if and only if q", and is abbreviated to "p iff q", or "p is equivalent

to q".

Alternatively, one can say"p is a necessary and sufficient condition for q".

If both p and q are true, or if both are false, then p , q is true. It is false

if (p is true and q is false), and it is also false if (p is false and q is true).

If p and q are statements, then the statement

p <=> q

is read as "p if and only if q", and is abbreviated to "p iff q", or "p is equivalent

to q".

Alternatively, one can say"p is a necessary and sufficient condition for q".

If both p and q are true, or if both are false, then p , q is true. It is false

if (p is true and q is false), and it is also false if (p is false and q is true).

.

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