Conjunction AND
In logic, a conjunction is a compound sentence formed by combining two sentences (or facts) using the word “and.”
A conjunction is true only when BOTH sentences (or facts) are true.
Examples:
- “Blue is a color and 7 + 3 = 10.” (T and T = T)
Since both facts are true, the entire sentence is true. - “One hour = exactly 55 minutes and one minute = exactly 60 seconds.”
(F and T = F) Since the first fact is false, the entire sentence is false. - “3 + 4 = 6 and all dogs meow.” (F and F = F)
Since both facts are false, the entire sentence is false.
Mathematicians often use symbols and tables to represent concepts in logic. The use of these variables, symbols and tables creates a shorthand method for discussing logical sentences.
A truth table is a pictorial representation of all of the possible outcomes of the truth value of a compound sentence. Letters such as p and q are used to represent the facts (or sentences) within the compound sentence.
Truth table for conjunction (and):
(notice the symbol used for “and” in the table below)
| p | q | p ∧ q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Remember: For a conjunction (and) to be true, BOTH facts must be true.