How do I formally express that a statement is true only if 3 propositions are true?
I have a rule: Action(A, B, C).
I want to say Action(A, B, C) is true only if:
1 - S is a member of set X.
2 - D is a member of set Y.
3 - T is a member of set Z.
I phrasing it at:
Action(A, B, C) only if 1, 2, and 3.
Is that correct and is there a more formal way to phrase this.
"$A$ only if $B$" is equivalent to $A\implies B$ by way of contraposition since this statement can be rephrased more explicitly as "if $B$ is not true then $A$ is not true". A way to phrase your original proposition without symbols is then:
If Action($A,B,C$) is true then 1, 2, and 3 are all true.