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# Euler diagrams, logic statements, and truth tables

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1. Create an Euler diagram to determine whether the syllogism is valid or invalid.

All grocery stores are open until 10 p.m.
The store on the corner is open until 10 p.m.
The store on the corner is a grocery store.

2. If the argument below is valid, name which of the four valid forms of argument is represented. If it is not valid, name the fallacy that is represented.

If I sing in the shower, then I will not be overheard while singing.
I was not overheard while singing.
Therefore, I sang in the shower.

3. Form the contrapositive: If I do not mow the lawn, the grass grows too tall

4. Construct a truth table for ~ (q V ~p)

https://brainmass.com/math/discrete-math/312410

#### Solution Preview

1. Create an Euler diagram to determine whether the syllogism is valid or invalid.

All grocery stores are open until 10 p.m.
The store on the corner is open until 10 p.m.
The store on the corner is a grocery store.

The argument is invalid because a store that is open until 10 p.m. does not have to be a grocery store.

See the attachment ...

#### Solution Summary

Euler diagrams, logic statements, and truth tables.

\$2.19

## Logic: Truth Tables, Conditional Statements, DeMorgan's Laws and Symbolic Form

1. Write the negation for the statement below.
No one in the family eats rhubarb

2. Let p, q, and r be the following statements:
p: Mike is sailing
q: Alice is on vacation
r: Sam is in town
Translate the following statement into English: (p &#61658; &#61566; q) &#61614; &#61566;r

3. Write the following compound statement in symbolic form
Let p: Today is Monday
q: Tomorrow is the day Sara leaves
If tomorrow is not the day Sara leaves, then today is Monday

4. Construct a truth table for &#61566; (p &#61658; q)

5. Write the converse, inverse, and contrapositive of the following conditional statement
If a dog is barking, then it will not bite

6. Determine whether the argument is valid or invalid.

A tree has green leaves or the tree does not produce oxygen.
This tree has green leaves
------------------------------------------------------------------------
&#61532; This tree does not produce oxygen.

7. Use Euler Diagrams to determine whether the following syllogism is valid or invalid.
Some senators are conservationists
No conservationists are pro-development
--------------------------------------------------
&#61532; Some senators are not pro-development

8. Determine the truth value of the statement &#61566;q &#61611; [ &#61566; r &#61657; (p &#61658; q)] when p is false, q is true, and r is true.

9. Determine the truth value of the following statement:
Rembrandt was a famous painter and some odd number are prime.

10. Use De Morgan's Laws to determine whether the two statements are equivalent
&#61566; (p &#61657; q), &#61566; (q &#61658; &#61566;p)

11. Determine which, if any, of the three statements are equivalent.
a) If today is Monday, then tomorrow is not Wednesday
b) It is false that today is Monday and tomorrow is not Wednesday
c) Today is not Monday or tomorrow is Wednesday

See attached for full problem description.

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