And,Or,IFF

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).
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