Question 1176925: Choose the best answer..
1.) Which statement has the same truth value in the statement,
“If the number is even, then it is divisible by two”?
a. If the number is divisible by two, then it is even.
b. If the number is not even, then it is not divisible by two.
c. If the number is not divisible by two, then it is not even.
2.) Given the statement, “If a polygon is pentagon, then it has five
sides”, what is the contrapositive?
a. If a polygon has five sides, then it is a pentagon.
b. If a polygon is not pentagon, then it has no five sides.
c. If a polygon has no five sides, then it is not a pentagon.
For items 3 -5, if p: A = πr2 and q: r = 10
3.) What statement is equivalent to q → p?
a. If r = 10, then A = πr2
b. If A ≠ πr2, then r ≠ 10
c. If r ≠ 10, then A ≠ πr2
4.) What statement is equivalent to ~q → ~p?
a. If r = 10, then A = πr2
b. If A ≠ πr2, then r ≠ 10
c. If r ≠ 10, then A ≠ πr2
5.) What statement is equivalent to ~p → ~q?
a. If r = 10, then A = πr2
b. If A ≠ πr2, then r ≠ 10
c. If r ≠ 10, then A ≠ πr2
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down each question:
**1.) Which statement has the same truth value in the statement, “If the number is even, then it is divisible by two”?**
* **Original statement:** If P, then Q (P: number is even, Q: number is divisible by two)
* We're looking for the **converse**, **inverse**, or **contrapositive** that has the same truth value as the original statement.
* The converse (Q -> P) is: If the number is divisible by two, then it is even.
* The inverse (~P -> ~Q) is: If the number is not even, then it is not divisible by two.
* The contrapositive (~Q -> ~P) is: If the number is not divisible by two, then it is not even.
* The original statement is true.
* The converse is true.
* The inverse is true.
* The contrapositive is true.
* The contrapositive always has the same truth value of the original statement.
* **Answer: c. If the number is not divisible by two, then it is not even.**
**2.) Given the statement, “If a polygon is pentagon, then it has five sides”, what is the contrapositive?**
* **Original statement:** If P, then Q (P: polygon is pentagon, Q: polygon has five sides)
* **Contrapositive:** If ~Q, then ~P (If not Q, then not P)
* **Answer: c. If a polygon has no five sides, then it is not a pentagon.**
**For items 3 -5, if p: A = πr2 and q: r = 10**
**3.) What statement is equivalent to q → p?**
* **q → p:** If q, then p (If r = 10, then A = πr2)
* **Answer: a. If r = 10, then A = πr2**
**4.) What statement is equivalent to ~q → ~p?**
* **~q → ~p:** If not q, then not p (If r ≠ 10, then A ≠ πr2)
* **Answer: c. If r ≠ 10, then A ≠ πr2**
**5.) What statement is equivalent to ~p → ~q?**
* **~p → ~q:** If not p, then not q (If A ≠ πr2, then r ≠ 10)
* **Answer: b. If A ≠ πr2, then r ≠ 10**
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