Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Suppose that P(n) is a propositional function...
Start Learning for Free
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)?
Most Upvoted Answer
Suppose that P(n) is a propositional function. Determine for which pos...
**Solution:**
To determine for which positive integers n the statement P(n) must be true, we need to analyze the given conditions and apply them iteratively.
**Given conditions:**
1. P(1) is true.
2. For all positive integers n, if P(n) is true then P(n+2) is true.
**Analysis:**
Let's start by analyzing the first condition:
1. P(1) is true.
Since P(1) is true, it means that the statement P(n) is true for at least one positive integer n, specifically n = 1.
Next, let's analyze the second condition:
2. For all positive integers n, if P(n) is true then P(n+2) is true.
This condition implies that if P(n) is true for any positive integer n, then P(n+2) must also be true. In other words, if P(k) is true for some positive integer k, then P(k+2) must also be true.
Since we know that P(1) is true, we can apply the second condition to determine the truth of P(n) for subsequent positive integers.
**Iterative Application:**
Starting with n = 1, we can iteratively apply the second condition to determine the truth of P(n) for subsequent positive integers:
- P(1) is true (given).
- P(3) must be true (applying the second condition to n = 1).
- P(5) must be true (applying the second condition to n = 3).
- P(7) must be true (applying the second condition to n = 5).
- P(9) must be true (applying the second condition to n = 7).
- ...
**Conclusion:**
Based on the given conditions and the iterative application of the second condition, we can conclude that the statement P(n) must be true for all positive odd integers n.
Therefore, the correct answer is:
**Oa. P(3)**
To determine for which positive integers n the statement P(n) must be true, we need to analyze the given conditions and apply them iteratively.
**Given conditions:**
1. P(1) is true.
2. For all positive integers n, if P(n) is true then P(n+2) is true.
**Analysis:**
Let's start by analyzing the first condition:
1. P(1) is true.
Since P(1) is true, it means that the statement P(n) is true for at least one positive integer n, specifically n = 1.
Next, let's analyze the second condition:
2. For all positive integers n, if P(n) is true then P(n+2) is true.
This condition implies that if P(n) is true for any positive integer n, then P(n+2) must also be true. In other words, if P(k) is true for some positive integer k, then P(k+2) must also be true.
Since we know that P(1) is true, we can apply the second condition to determine the truth of P(n) for subsequent positive integers.
**Iterative Application:**
Starting with n = 1, we can iteratively apply the second condition to determine the truth of P(n) for subsequent positive integers:
- P(1) is true (given).
- P(3) must be true (applying the second condition to n = 1).
- P(5) must be true (applying the second condition to n = 3).
- P(7) must be true (applying the second condition to n = 5).
- P(9) must be true (applying the second condition to n = 7).
- ...
**Conclusion:**
Based on the given conditions and the iterative application of the second condition, we can conclude that the statement P(n) must be true for all positive odd integers n.
Therefore, the correct answer is:
**Oa. P(3)**
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Top Courses for Computer Science Engineering (CSE)View all
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)?
Question Description
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)?.
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)?.
Solutions for Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? defined & explained in the simplest way possible. Besides giving the explanation of
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)?, a detailed solution for Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? has been provided alongside types of Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? theory, EduRev gives you an
ample number of questions to practice Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n + 2) is true. Oa. P(3) Ob. P(4) OCP P(6) Od. P(2)? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup