D421 Discrete Math: Functions and Relations - Set 2 - Part 1

Test your knowledge of technical writing concepts with these practice questions. Each question includes detailed explanations to help you understand the correct answers.

Question 1: What is a proposition in logic?

A declarative statement that is either true or false

A question

A command

An undefined expression

Question 2: What does the logical conjunction (AND, ∧) require to be true?

At least one operand must be true

Both operands must be true

Both operands must be false

Exactly one operand is true

Question 3: What does the logical disjunction (OR, ∨) require to be true?

Both operands must be true

Both operands must be false

At least one operand must be true

Neither operand is true

Question 4: What does negation (NOT, ¬) do to a proposition?

Leaves it unchanged

Makes it always true

Makes it a question

Reverses its truth value

Question 5: When is the conditional p → q false?

When p is true and q is false

When both are true

When both are false

When p is false

Question 6: What is the converse of the conditional p → q?

¬p → ¬q

q → p

¬q → ¬p

p → ¬q

Question 7: What is the contrapositive of p → q?

q → p

¬p → ¬q

¬q → ¬p

p → q

Question 8: A conditional statement is logically equivalent to its:

Converse

Inverse

Negation

Contrapositive

Question 9: What is a biconditional p ↔ q true?

When p and q have the same truth value

When p and q differ

When p is true only

When both are false only

Question 10: What is a tautology?

A statement that is always false

A statement that is always true

A statement sometimes true

A contradiction

Question 11: What is a contradiction in logic?

A statement that is always true

A statement sometimes true

A statement that is always false

A tautology

Question 12: According to De Morgan's laws, ¬(p ∧ q) is equivalent to:

¬p ∧ ¬q

p ∨ q

¬p → ¬q

¬p ∨ ¬q

Question 13: According to De Morgan's laws, ¬(p ∨ q) is equivalent to:

¬p ∧ ¬q

¬p ∨ ¬q

p ∧ q

p → q

Question 14: How many rows does a truth table with n propositional variables have?

n^2

2^n

Question 15: What does the universal quantifier (∀) mean?

There exists an element

For no elements

For all elements

For exactly one element

Question 16: What does the existential quantifier (∃) mean?

For all elements

For no elements

For every pair

There exists at least one element

Question 17: What is the negation of the statement 'for all x, P(x)'?

There exists x such that not P(x)

For all x, not P(x)

There exists x such that P(x)

P(x) is always true

Question 18: What is the negation of 'there exists x such that P(x)'?

There exists x such that not P(x)

For all x, not P(x)

For all x, P(x)

P(x) is sometimes true

Question 19: What is a direct proof?

Assuming the conclusion is false

Testing a few examples

Assuming the hypothesis and deriving the conclusion through logical steps

Using a counterexample

Question 20: What is a proof by contradiction?

Proving the contrapositive

Checking all cases

Giving an example

Assuming the statement is false and deriving a contradiction

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