Conditional Statements

• 1. Abbreviate the elements that make up the statement.
• 2. Symbolize the statement using an arrow.
• 3. Symbolize the statement’s contrapositive.

A conditional statement is a statement that says, “If (condition), then (consequence).”

“if”—goes in front of the arrow. The consequence—the statement that follows “then”—goes behind the arrow. So, “If something is an apple, then it is a fruit” becomes “A → F.”

• 1. Flip sides. Take the element before the arrow and move it after the arrow. Take the element after the arrow and move it before the arrow.
• 2. Flip signs. Take any element that is positive and negate it.
• 3. Flip connectors. “And” becomes “or,” and “or” becomes “and.” Take any “&” and make it a “/.” Take any “/” and make it an “&.”
• Take any element that is negative and make it positive.Thus, the contrapositive of “A→F” is “~F→~A”.
• Example: Start with the statement, “If not A or B, then C and not D.” You can symbolize that statement using your standard “~” as a negative and the “&” and “/” signs for “and” and “or,” respectively:~A/B—C &~D

• B only if A = B → A 
• only if” language, whatever comes after the “only if” is placed behind the arrow.
• Not B unless A= ~B → A  
• 1. Take what follows “unless” and make it the back half of your symbolization.
• 2. Take what comes before the “unless,” negate it, and make it the front half of your symbolization.
• "All A are B" = A → B
• "No A are B" = A → ~B
• "B if, but only if, A" = A → B and B → A
• B if A”; and (2) “B only if A”—disguised as one.