Question $1$: True$/$false question $(0\mathrm{.}3$ points$)$:

a$.$ A contradiction is a statement that is always false, regardless of the truth values of its

components.

b$.$ The logical disjunction $($OR$)$ of a tautology and a contradiction is a tautology.

Your answer: True or false? Please write it down here:

Question $2$: Multiple choice question $(0\mathrm{.}6$ points$)$:

Which of the following statements is an example of a contingency?

c$."$If it is daytime, then it is nighttime."

d$."$If it is daytime, then it is sunny."

e$."$If it is nighttime, then it is dark."

f$."$If it is nighttime, then it is daytime."

Your answer: Choose the best answer and write it down here:

Question $3$: Open question $(0\mathrm{.}9$ points$)$:

Demonstrate a propositional equivalence between two statements and explain the reasoning

behind their equivalence.

Your answer: Please answer the questions in a few lines or paragraphs.

Question $4$: Challenging question: $(1\mathrm{.}2$ points$)$:

The propositional boolean operator "exclusive or$,"$ often represented as XOR and written as

$"$

$",$ is a logical operator that applies to two propositions and returns true if exactly one of the

propositions is true and false otherwise. Also, the negation of XOR is the logical biconditional.

Use the truth table to prove