Lauren B. answered • 10/07/19
French and English Language Arts Tutor
The truth value is False.
First determine the connective with the greatest scope (here it would be the conjunction). This statement is a conjunction with a conditional inside of it, so you know that you must (1) determine the truth value of the conditional first and then (2) determine the truth value of the conjunction. Then use your truth table for conditionals and conjunctions.
Truth Table for Conditionals (->) and Conjunctions (&/ ∙):
| P | Q | P → Q | P ∙ Q |
| T | T | T | T |
| T | F | F | F |
| F | T | T | F |
| F | F | T | F |
A & (B->C) looks like T & (T->F)
B->C is rewritten as T->F, and T->F is always False (the only conditional statement that can be false). Once you have determined that the truth value of B->C is false, you see that any conjunction (AND statement) with either conjunct being false, must have a truth value of FALSE, regardless of the truth value of the other conjunct (in other words, BOTH conjuncts must be true in order for the whole conjunction to be true).
| A | & | ( | B | -> | C | ) | |
| T | T | F | |||||
| Step 1 | T | F | |||||
| Step 2 | F |
N.B.: -> is another symbol for the conditional and & is another symbol for the conjunction.
