Reasoning and Logic

Which of the following is the contrapositive of  $p\rightarrow q$  ?

•  $\sim p\rightarrow\sim q$  

•  $\sim q\rightarrow\sim p$  

•  $q\rightarrow p$  

•  $p\rightarrow\sim q$  

Which of the following is the converse statement of: "If Bill does not drive quickly, he will be late"

• If Bill is late, then he did not drive quickly

• If Bill drives quickly, then he will not be late

• If Bill is late, then he drove quickly

• If Bill is not late, then he drove quickly

The compound proposition  $\left(p\vee\sim q\right)\rightarrow p$  is an example of:

• a contradiction

• a tautology

• a contingency

• an affirmative statement 

When all output values of a proposition are true, the proposition is said to be

• logically equivalent

• a contradiction

• a tautology

• a contingency

The proposition $\left(\sim p\vee q\right)\wedge p$  simplifies to:

•  $p\wedge q$  

•  $\sim p\vee q$  

•  $\sim\left(p\wedge q\right)$  

•  $p\vee q$  

What is the truth value of the following statement: If Barcelona is a city in Spain, then Milan is not a city in Germany.

• 0

• 1

• 0 and 1

• 0 or 1

p = Mervyn is a farmer

q= Mervyn wears a brown hat

r = All farmers wear a brown hat

Express in symbolic form: If Mervyn is a farmer, then he wears a brown hat."

• $p\longleftrightarrow q$

• $q\rightarrow p$

• $\sim q\rightarrow\sim p$

• $p\rightarrow q$

p = Mervyn is a farmer

q= Mervyn wears a brown hat 
r = All farmers wear a brown hat

Express in words the proposition:  $\left(r\wedge q\right)\longrightarrow p\$  

• If all farmers wear a brown hat and Mervyn is a farmer, then Mervyn wears a brown hat. 

• If all farmers wear a brown hat and Mervyn wears a brown hat, then Mervyn is a farmer

• If all farmers wear a brown hat or Mervyn is a farmer, then Mervyn wears a brown hat. 

• If all farmers wear a brown hat or Mervyn wears a brown hat, then Mervyn is a farmer

Two compound propositions are said to be logically equivalent if:

• For any combination of input values, the output value is always zero.

• For any combination of input values, the output value is always 1

• Both propositions produce identical output values

• They can both be simplified.

Which of the following shows the most appropriate way of setting up a truth table for $p\vee\left(\sim q\rightarrow p\right)$  ?

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