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Truth Tables and Translation in Symbolic Form

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1. Determine whether ~ [~ (p V ~q) <=> p V ~q. Explain the method(s) you used to determine your answer.

2. Translate the following argument into symbolic form. Determine whether the argument is valid or invalid. You may compare the form of the argument to one of the standard forms or use a truth table.

If Spielberg is the director, then the movie should be good.
Spielberg didn’t direct the movie, so it probably isn’t good.

4. Construct one truth table that contains truth values for all of the given statements and determine which of the statements, if any, are logically equivalent.

(a) (~p) V (~q) (b) (~p) ^ (~q) (c) ~(p V q)

5. Use the following statements for p and q to illustrate De Morgan’s laws.
p: The moon is round
q: The night is dark.

6) Use Euler diagrams to determine the validity of the arguments
All squares are rectangles
Therefore, all squares are equilateral.

https://brainmass.com/math/discrete-math/truth-tables-translation-symbolic-form-113305

Solution Summary

The solution contains the answers to various questions in mathematical logic concerning De Morgan's Laws, validity of arguments, symbolic forms etc.

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Truth Table Statement and Argument

Write the statements in symbolic form
p: The temperature is 90deg.
q: The air conditioner is working
r: The apartment is hot.

In exercises 7-16 construct a truth table for the statements:
~ (~p←>q)

Sec. 3.5 #40
Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
If you pass general chemistry, then you can take organic chemistry.
You pass general chemistry
You can take organic chemistry.

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