Conjunction AND

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:

1. “Blue is a color and 7 + 3 = 10.” (T and T = T)
   Since both facts are true, the entire sentence is true.
2. “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. “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)

Remember: For a conjunction (and) to be true, BOTH facts must be true.

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