Consider the following theorem. Theorem: For all sets A and B, if A ⊆ B, then A ∪ B ⊆ B. Supply explanations for the steps in the proof of the theorem. Proof: Statement
Explanation Suppose A, B, and C are any sets such that A ⊆ B. starting point We must show that A ∪ B ⊆ B. conclusion to be shown Let x be any element in A ∪ B.
start of an element proof Then x is in A or x is in B.
In case x is in A, then x is in B
In case x is in B, then x is in B.
tautology (p → p) So in either case, x is in B. proof by division into cases Thus every element in A ∪ B is in B.
since x could be any element of A ∪ B Therefore, A ∪ B ⊆ B [as was to be shown]."

step-by-step :

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

need more detail

step-by-step explanation:

lele