Definition : A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by p ∨ q . A disjunction is false if and only if both statements are false; otherwise it is true. The truth values of p ∨ q are listed in the truth table below.A disjunction, both statements must be false for the disjunction to be false.
Example 1: |
Given: | p: Ann is on the softball team. |
q: Paul is on the football team. |
Problem: | What does p ∨ q represent? |
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Solution: In Example 1, statement p represents, "Ann is on the softball team"
and statement q represents, "Paul is on the football team." The symbol ∨
is a logical connector which means "or." Thus, the compound
statement p ∨ q represents the sentence, "Ann is on the softball team or
Paul is on the football team." The statement p ∨ q is a disjunction.
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p | q | p ∨ q |
T | T | T |
T | F | T |
F | T | T |
F | F | F |
Given: | a: A square is a quadrilateral. |
b: Harrison Ford is an American actor. |
Problem: | Construct a truth table for the disjunction "a or b." |
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Solution: |
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Example 3: |
Given: | r: x is divisible by 2. |
s: x is divisible by 3. |
Problem: | What are the truth values of r ∨ s |
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Solution: | |
If x = 6, then r is true, and s is true. The disjunction r ∨ s is true.
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If x = 8, then r is true, and s is false. The disjunction r ∨ s is true. |
If x = 15, then r is false, and s is true. The disjunction r ∨ s is true. |
If x = 11, then r is false, and s is false. The disjunction r ∨ s is false. |
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