"conjunction" "disjunction" "implication" "equivalence"
    "A and B" "A or B" "A implies B" "A is equivalent to B"
A B A B A B A B A B
T T        
T F        
F T        
F F        
           
Alternative

Phrases

"A also B"

"A, but B"

"A. In addition B"

"A inclusive or B" "If A, then B"

"B follows from A"

"A is a sufficient

condition for B"

"B is a necessary condition for A"

"A only if B"

"A if and only if B"

"A iff B"

"A is necessary and sufficient for B"

           
Operand Names "conjuncts" "disjuncts" "antecedent"

"consequent"

 

"A or B" questions:

If A is true and B is true, what truth value would you assign to A B?

If A is true and B is false, what truth value would you assign to A B?

If A is false and B is true, what truth value would you assign to A B?

If A is false and B is false, what truth value would you assign to A B?

"A implies B" Questions:

If A is true and B is true, what truth value would you assign to A B?

If A is true and B is false, what truth value would you assign to A B?

If A is false and B is true, what truth value would you assign to A B?

If A is false and B is false, what truth value would you assign to A B?

More "A implies B" Questions:

If A B is true and A is true, what truth value must B have?

(Therefore, we say "A is a for B")

If A B is true and B is false, what truth value must A have?

(Therefore, we say "B is for A")