Discrete Mathematics & Logic

Which of the following is a correct representation of the logical statement "If it rains, then the ground is wet" using implication symbols?

Given sets $A = \{1,2,3\}$ and $B = \{2,3,4\}$, what is the result of $A \cap B$ (the intersection of $A$ and $B$)?

How many distinct 3-letter permutations can be formed from the letters $\{A, B, C, D\}$ without repetition?

In a connected graph with $n$ vertices and $n-1$ edges, which statement is always true?

To prove that $\sqrt{2}$ is irrational using proof by contradiction, which is the correct first assumption?

In combinatorics, what does the binomial coefficient $\binom{n}{k}$ represent?

The union of two sets $A$ and $B$ contains all elements that are in $A$, in $B$, or in both.

In a simple graph, the sum of the degrees of all vertices is equal to twice the number of edges.

A proof by induction requires proving the base case and the inductive step to conclude the statement holds for all natural numbers.

Which of the following is a valid argument form in propositional logic known as Modus Ponens?