Q1. Propositional Logic and its Applications
1. Let p and q be the propositions "Swimming at the New Jersey shore is allowed" and
"Sharks have been spotted near the shore," respectively. Express each of these compound
propositions as an English sentence.
a. $\neg p \to \neg q$
b. $\neg p \land (p \lor \neg q)$
2. Construct a truth table for the compound proposition.
$(p \leftrightarrow q) \oplus (\neg p \leftrightarrow \neg r)$
3. Proof
Prove that if n is a positive integer, then n is odd if and only if 5n + 6 is odd.
Q2. Sets and Set Operations
1. Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10). Find
$(A \cup B) \cap C$
Q3. Functions
1. Determine whether each of these functions is a bijection from R to R.
a. f(x) = 2x + 1
b. f(x) = x^2 + 1