1.
Another name for an if-then statement is a _______? Every conditional has two parts. The part following if is the _______?, and the part following then is the _______? (In-order)
Correct Answer
D. Conditional; hypothesis; conclusion
Explanation
An if-then statement is also known as a conditional. The part following if is the hypothesis, which is the condition or the statement that is being tested. The part following then is the conclusion, which is the result or the action that will occur if the hypothesis is true. Therefore, the correct order is conditional; hypothesis; conclusion.
2.
Which of the following choices shows a true conditional with the hypothesis and conclusion identified correctly?
Conditional Statement
If yesterday was Wednesday, then tomorrow is Friday.
Correct Answer
A. Hypothesis: Yesterday was Wednesday. conclusion: Tomorrow is Friday.
Explanation
They all may sound right, but choose carefully and look carefully at the question!
3.
What is the contra-positive of "If it is Thursday, then Terrence has basketball practice".
Correct Answer
C. If Terrence does not have basketball practice, then it is not Thursday.
Explanation
The contra-positive of a conditional statement switches the hypothesis and conclusion and negates both. In the given statement, the original conditional statement is "If it is Thursday, then Terrence has basketball practice." The contra-positive of this statement is "If Terrence does not have basketball practice, then it is not Thursday."
4.
Solve for χ. (12χ + 7χ=23)
Correct Answer
C. 1.21
Explanation
To solve for χ, we need to combine the like terms on the left side of the equation. Adding 12χ and 7χ gives us 19χ. So the equation becomes 19χ = 23. To isolate χ, we divide both sides of the equation by 19. This gives us χ = 23/19, which is approximately equal to 1.21. Therefore, the correct answer is 1.21
5.
- There are no dancers that aren't slim.
- There are no singers that aren't dancers.
Which statement must be true based on these two statements??
Correct Answer
A. All singers are slim.
Explanation
Based on the given statements, it can be concluded that all singers are slim. This is because the first statement states that there are no dancers that aren't slim, and the second statement states that there are no singers that aren't dancers. Since there are no dancers who are not slim, and all singers are dancers, it can be inferred that all singers must also be slim.
6.
- All dogs are mammals.
- All mammals are warm-blooded. Which statement must be true based on these two statements?
Correct Answer
A. All dogs are warm-blooded.
Explanation
Based on the given statements, it can be concluded that all dogs are mammals and all mammals are warm-blooded. Therefore, it must be true that all dogs are warm-blooded.
7.
All crows are black. All black birds are loud. All crows are birds.
Statement can be made: All crows are loud.
Correct Answer
A. True
Explanation
Based on the given statements, we know that all crows are black, all black birds are loud, and all crows are birds. Since all crows are birds and all black birds are loud, it can be concluded that all crows are loud. Therefore, the statement "All crows are loud" is true.
8.
Mike finished ahead of Paul. Paul and Brian both finished before Liam. Owen did not finish last. Who was the last to finish?
Correct Answer
C. Liam
Explanation
Based on the given information, Mike finished ahead of Paul, and Paul and Brian both finished before Liam. Since Owen did not finish last, the only option left is Liam. Therefore, Liam was the last to finish.
9.
When is an inference deductively valid?
Correct Answer
A. Its conclusion follows logically from its premises.
Explanation
An inference is deductively valid when its conclusion follows logically from its premises. This means that the conclusion can be logically derived or inferred from the given premises. In other words, if the premises are true, then the conclusion must also be true based on the rules of logic. This is the fundamental principle of deductive reasoning, where the truth of the premises guarantees the truth of the conclusion.
10.
A is equal to B. B is also equal to C. Then we can conclude
Correct Answer
A. A is equal to C
Explanation
If A is equal to B and B is equal to C, then it can be concluded that A is equal to C. This is because if A is equal to B and B is equal to C, then transitive property of equality states that A must be equal to C as well.