Math Problem Statement
answer the true one
Solution
Let’s analyze the provided question and solve it step-by-step:
Problem Summary:
-
Let : "15 is an odd number"
This is true because 15 is indeed an odd number. -
Let : "21 is a prime number"
This is false because 21 is not a prime number (it can be factored as ).
We now evaluate each logical statement based on being true and being false.
Logical Statements to Evaluate:
-
(p OR q):
- OR is true if at least one of or is true.
- Here, is true and is false.
- .
-
(p AND q):
- AND is true only if both and are true.
- Here, is true but is false.
- .
-
(p implies q):
- Implication is false only if is true and is false.
- Here, is true and is false.
- .
-
(NOT q implies p):
- First, evaluate (NOT q). Since is false, is true.
- Implication is true if is true or is true.
- Both and are true.
- .
Correct Statement:
From the evaluation above:
Thus, the correct statements are and .
Let me know if you’d like further clarification!
Related Questions:
- What is the difference between conjunction () and disjunction () in logic?
- Can you explain why is false in this case?
- How is the truth value of an implication () determined in logic?
- What are prime numbers, and why is 21 not prime?
- How would the answers change if were true instead?
Tip:
In logic, implications are tricky because they are true except when is true and is false. Always evaluate implications carefully!
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Math Problem Analysis
Mathematical Concepts
Logic
Propositional Calculus
Truth Tables
Formulas
Logical OR (p ∨ q)
Logical AND (p ∧ q)
Implication (p ⇒ q)
Negation (¬q)
Implication (¬q ⇒ p)
Theorems
Truth Table for Propositional Logic
Evaluation of Logical Connectives
Suitable Grade Level
Grades 9-12