Math Problem Statement

Which of the following is a disjunction of p and q? Responses

A p ∧ qp  ∧  q

B p ⊕ qp  ⊕  q

C p → qp → q

D p ∨ q

Solution

The correct answer is D: p ∨ q.

A disjunction in logic refers to the logical "or" (denoted by ). It is true if at least one of the propositions is true. So, in this case, p ∨ q represents the disjunction of p and q.

Here are explanations for the other options:

  • A: p ∧ q is a conjunction (logical "and").
  • B: p ⊕ q represents an exclusive or (XOR).
  • C: p → q is an implication (if p then q).

Would you like more details or have any questions about disjunctions or logical operators?

Here are 5 related questions to expand on this:

  1. What is the difference between conjunction and disjunction in logic?
  2. How does the truth table for a disjunction (p ∨ q) look?
  3. What is the meaning of exclusive or (XOR) in logic?
  4. How does the truth table for p → q (implication) compare to that for p ∨ q (disjunction)?
  5. Can a disjunction (p ∨ q) ever be false? When?

Tip: In propositional logic, a disjunction is true if at least one of the statements is true, but a conjunction is true only if both statements are true.

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Math Problem Analysis

Mathematical Concepts

Propositional Logic
Logical Operators

Formulas

p ∨ q (disjunction)

Theorems

Disjunction in logic: A disjunction is true if at least one of the propositions is true.

Suitable Grade Level

Grades 9-12