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Chapter 3: Problem 16

Use De Morgan's laws to write a statement that is equivalent to the given statement. It is not true that Martin Luther King, Jr. supported violent protest or the Vietnam War.

Short Answer

Expert verified
The equivalent statement using De Morgan's Laws is 'Martin Luther King, Jr. did not support violent protest and he did not support the Vietnam War'.

Step by step solution

01

Identifying the components of the statement

To begin, we identify the main components of this statement: \n\n 1. The phrase 'Martin Luther King, Jr. supported violent protest' represents the first proposition, which we can label as P. \n\n 2. The phrase 'The Vietnam War' represents the second proposition, which we can express as Q.
02

Applying De Morgan's Laws

The original statement can be symbolically represented as 'not (P or Q)'. Applying De Morgan's Laws would result in 'not P and not Q'.
03

Reformulating the Statement

Return to the original sentence and replace P and Q with the suitable phrases. According to De Morgan's Laws, the equivalent statement to 'It is not true that Martin Luther King, Jr. supported violent protest or the Vietnam War' would be 'Martin Luther King, Jr. did not support violent protest and he did not support the Vietnam War'.

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