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:
- What is the difference between conjunction and disjunction in logic?
- How does the truth table for a disjunction (p ∨ q) look?
- What is the meaning of exclusive or (XOR) in logic?
- How does the truth table for p → q (implication) compare to that for p ∨ q (disjunction)?
- 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