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Chapter 3: Problem 24

Use De Morgan's laws to write a statement that is equivalent to the given statement. If it is Saturday or Sunday, I do not work.

Short Answer

Expert verified
The equivalent statement, using De Morgan's laws, to 'If it is Saturday or Sunday, I do not work' is 'It is not Saturday and it is not Sunday'.

Step by step solution

01

Identify the Logical Components

Break down the original statement into its basic logical components. In this case, we have two propositions: 'It is Saturday' and 'It is Sunday'. The negative phrase 'I do not work' suggests that these propositions are negated. So, the original statement 'If it is Saturday or Sunday, I do not work' can be expressed as 'NOT(Saturday OR Sunday)'. This is our starting point.
02

Apply De Morgan鈥檚 Law

The De Morgan's laws state that the negation of a disjunction (OR) is the conjunction (AND) of the negations. In symbolic terms, 'NOT(P OR Q)' is equivalent to '(NOT P) AND (NOT Q)'. Using this law, the statement 'NOT(Saturday OR Sunday)' can be transformed into '(NOT Saturday) AND (NOT Sunday)'.
03

Form the Equivalent Statement

Now we convert the transformed expression '(NOT Saturday) AND (NOT Sunday)' back into a sentence in the natural language. Hence, the phrase becomes 'It is not Saturday and it is not Sunday'. This is equivalent to the original statement that 'If it is Saturday or Sunday, I do not work' based on De Morgan's laws.

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