Match the scenario with the law of logic it illustrates. Question 1 options:

__Law of Syllogism

__Not a valid conclusion has been made.

__Law of Contrapositive

__Law of Detachment

1.
If it is raining, I will use an umbrella.

It is raining.

Therefore, I will use an umbrella.

2.
If the sun sets, it will be dark outside.

It is not dark outside.

Therefore, the sun hasn't set yet.

3.
If I do well on my assignments, my grade will improve.

If my grade improves, my parents will be happy.

Therefore, if I do well on my assignments, my parents will be happy.

4.
If I cook dinner, my daughter will eat.

My daughter ate.

Therefore, I cooked dinner.

I just took this and got an A, so here are the answers :)

Make sure to take notes or put this with your notes! :))

Law of Syllogism: 3

If I do well on my assignments, my grade will improve.

If my grade improves, my parents will be happy.

Therefore, if I do well on my assignments, my parents will be happy.

Not a valid conclusion has been made: 4

If I cook dinner, my daughter will eat.

My daughter ate.

Therefore, I cooked dinner.

Law of contrapositive : 2

If the sun sets, it will be dark outside.

It is not dark outside.

Therefore, the sun hasn't set yet

Law of Detachment: 1

If it is raining, I will use an umbrella.

It is raining.

Therefore, I will use an umbrella.

explanation:

Syllogism:

p → q and q → r then p → r is also true.

Contrapositive:

If not q, then not p.

Detachment:

If p , then q

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)