2.6 De Morgan’s Laws

Turning the negation of an and-statement into an or-statement and back, negating a conditional, and confirming both rules by truth table.

Contemporary Mathematics, 2.6 De Morgan’s Laws

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5 exercises

2.6 Exercise 1

Write the negation of each statement in words without using the phrase, “It is not the case that.”

Kristin is a biomedical engineer and Thomas is a chemical engineer.
A person had cake or they had ice cream.

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2.6 Exercise 3

Write the negation of each conditional statement.

If Adele won a Grammy, then she is a singer.
If Henrik Lundqvist played professional hockey, then he did not win the Stanley Cup.

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2.6 Exercise 5

Write the negation of each conditional statement.

If all cats purr, then my partner’s cat purrs.
If a penguin is a bird, then some birds do not fly.

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2.6 Exercise 7

Write the negation of each conditional statement applying De Morgan’s Law.

If mom needs to buy chips, then Mike had friends over and Bob was hungry.
If Juan had pizza or Chris had wings, then dad watched the game.

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2.6 Exercise 9

Construct a truth table to verify De Morgan’s Law for the negation of a conjunction, $\sim \left(p \land q\right) \text{ } \equiv \text{ } \sim p \lor \sim q$ , is valid.

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