Conditional statements and laws. 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.

ANSWER OPTIONS:
Law of Detachment, not a valid conclusion has been made, Law of Syllogism, Or Law of Contrapositive.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

9

step-by-step explanation:

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: