write the biconditional for p then q if q then p remember to use the phrase if and only if to combine the orginal statement and its converse
The biconditional statement for "If p then q" and "If q then p" is:
"P if and only if q"
or
"P ↔ q"
To write the biconditional for "p then q if q then p," we can combine the original statement and its converse using the phrase "if and only if."
The original statement is:
p then q (p → q)
The converse of the original statement is:
q then p (q → p)
Combining these statements, the biconditional becomes:
p if and only if q (p ↔ q)
To write the biconditional for the statements "p then q" and "q then p," we can combine them using the phrase "if and only if."
The original statement "p then q" can be written as "p → q."
The converse of "p then q" is "q → p."
To combine these statements using "if and only if," we can use the symbol "↔" which represents biconditional.
So, the biconditional statement for "p then q" if "q then p" would be:
"p → q ↔ q → p"
This means that p will be true if and only if q is true, and q will be true if and only if p is true.