# logic – What is the Number of Possible Nonequivalent Propositions with \$P_1, P_2, P_3\$ Using \$iff\$ Operator?

You just need to use $$P_1$$, $$P_2$$, $$P_3$$ and $$Leftrightarrow$$ symbols, for example $$P_2$$ is a formula, $$(P_1 Leftrightarrow P_3) Leftrightarrow P_2$$ is a formula. As stated in the question, you must not use $$vee$$, $$wedge$$ or $$neg$$.

You need to find the number of non-equivalent formulae. For example, $$P_1$$ is equivalent to $$P_1Leftrightarrow P_1$$, but $$P_1Leftrightarrow P_2$$ is not equivalent to $$P_1 Leftrightarrow P_3$$.