Boolean variables

A Boolean variable is either true or false. In Python, these are written in the following way:

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p = True
 
q = False
 
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Boolean values appear when doing comparisons. Try the following:

Boolean values also determine the behavior of if/else statements and while loops.

Logical Operators

(a)

The negation operator:

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not p
      
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(b)

The AND operator:

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p and q
      
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(c)

The OR operator:

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p or q
      
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Problems

(a)

With $p$ true and $q$ false, compute the truth value of the following:

(i)

$p\vee q$

(ii)

$p\to q$ (Hint: There is no conditional operator, so use an equivalent form)

(iii)

$(p\to q)\wedge \neg q$

(iv)

$p\to (q\wedge \neg q)$

(b)

Use the code here to construct truth tables for the following problems:

(i)

Construct a truth table for $\neg p \vee q$.

(ii)

Construct a truth table for $(p \vee q) \vee r$.

(iii)

Construct a truth table that shows that $\neg (p \vee q) \equiv \neg p \wedge \neg q$.