Logical Equivalence & De Morgan's Laws (Discrete Mathematics)
Free printable Discrete Mathematics worksheet on logical equivalence: De Morgan's laws, negating implications, and deciding whether two propositions are equivalent, with every verdict checked against the full truth tables.
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Discrete Mathematics · Math worksheet
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Logical Equivalence & De Morgan's Laws
Two propositions are logically equivalent when they have identical truth tables. Use De Morgan's laws, ¬(p ∧ q) is equivalent to ¬p ∨ ¬q and ¬(p ∨ q) is equivalent to ¬p ∧ ¬q, together with double negation and the implication law p → q is equivalent to ¬p ∨ q. When two formulas are not equivalent, find one assignment where they disagree.
Word bank
NoYesQ ∧ rP ∧ ¬q¬p ∨ ¬q¬p ∨ ¬r
- 1.Use De Morgan's laws to rewrite ¬(p ∧ q) so that negation is applied only to individual variables.
- 2.Use De Morgan's laws to rewrite ¬(¬q ∨ ¬r) so that negation is applied only to individual variables.
- 3.Use De Morgan's laws to rewrite ¬(p ∧ r) so that negation is applied only to individual variables.
- 4.Write the negation of p → q as an equivalent proposition that does not use → or a leading negation.
- 5.Write the negation of q → ¬r as an equivalent proposition that does not use → or a leading negation.
- 6.Are ¬(p ∧ q) and ¬p ∨ ¬q logically equivalent? Answer Yes or No.
- 7.Are p → q and ¬q → ¬p logically equivalent? Answer Yes or No.
- 8.Are p → q and q → p logically equivalent? Answer Yes or No.
- 9.Are ¬(p ∧ q) and ¬p ∧ ¬q logically equivalent? Answer Yes or No.
- 10.Are p ∧ (q ∨ r) and (p ∧ q) ∨ (p ∧ r) logically equivalent? Answer Yes or No.
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