WGU C959: Discrete Math I (Unit 1)
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1. Order of operations: 1. ¬ (not)
2. '(and)
3. ((or)
2. Converse of p ’ q: q ’p (switch)
3. Contrapositive of p ’ q: ¬q ’¬p (negative switch)
4. Inverse of p ’ q: ¬p ’¬q (negative)
5. Biconditonal statement: p ”q
The proposition p ”q is true when p and q have the same truth value and is false when p and q have different truth
values. (if and only if)
6. Tautology: the proposition is always true, regardless of the truth value of the individual propositions that occur
in it.
7. Contradiction: the proposition is always false, regardless of the truth value of the individual propositions that
occur in it.
8. Predicate: A logical statement whose truth value is a function of one or more variables - P(x)
9. Free variable vs. Bound variable: x in the predicate P(x) is free to take any value in the domain
x in the statement x P(x) is bound to a quantifier
10. De Morgan's law for quantified statements: ¬x F(x) ax ¬F(x)
and
¬x P(x) ax ¬P(x)
11. Nested quantifiers: xy M(x,y) - For every pair of x and y, M(x,y) is true
xy M(x,y) - There exists at least one pair of x and y such that M(x,y) is true
xy M(x,y) - There exists at least one x that pairs with ALL y, such that M(x,y) is true
xy M(x,y) - For each x, there is at least one y, such that M(x,y) is true
12. De Morgan's law with nested quantifiers: All quantifiers flip
1/3
Study online at https://quizlet.com/_i20bam
1. Order of operations: 1. ¬ (not)
2. '(and)
3. ((or)
2. Converse of p ’ q: q ’p (switch)
3. Contrapositive of p ’ q: ¬q ’¬p (negative switch)
4. Inverse of p ’ q: ¬p ’¬q (negative)
5. Biconditonal statement: p ”q
The proposition p ”q is true when p and q have the same truth value and is false when p and q have different truth
values. (if and only if)
6. Tautology: the proposition is always true, regardless of the truth value of the individual propositions that occur
in it.
7. Contradiction: the proposition is always false, regardless of the truth value of the individual propositions that
occur in it.
8. Predicate: A logical statement whose truth value is a function of one or more variables - P(x)
9. Free variable vs. Bound variable: x in the predicate P(x) is free to take any value in the domain
x in the statement x P(x) is bound to a quantifier
10. De Morgan's law for quantified statements: ¬x F(x) ax ¬F(x)
and
¬x P(x) ax ¬P(x)
11. Nested quantifiers: xy M(x,y) - For every pair of x and y, M(x,y) is true
xy M(x,y) - There exists at least one pair of x and y such that M(x,y) is true
xy M(x,y) - There exists at least one x that pairs with ALL y, such that M(x,y) is true
xy M(x,y) - For each x, there is at least one y, such that M(x,y) is true
12. De Morgan's law with nested quantifiers: All quantifiers flip
1/3
