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

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

answer: 8 years

step-by-step explanation:

the explanation is that in 8 years the child will be 20 and in 8 years the father will be 40 and 20 is half of 40.