Prove: forall a, b, c elementof z, if a does not divide bc, then a does not divide b.

Answer with explanation:

It is given that , a,b and c are three elements of Z.Where Z is set of Integers.

It is also given that, a does not divide bc.

⇒We will use following theorem to prove this.

If a divides b, it means

¬ b= ma

where , m is an integer.

--As, a,  does not divide bc, then, b c will not be integral multiple of a.

That is, b c≠ k a

→Suppose factor of bc are=1, s, s h, s²h,s²h²,s³h,,b,c.

Neither of the factors of bc will be divisible by a.

→It means (bc ,a) are coprime.

For example (7,9) are coprime.

Factors of 9 are =1, 3, 9

So, (7,3) will be also coprime.

→So, all the factors of bc ,which is equal to ={1, s, s h,s²h,s²h²,s³h,,b,c} will be coprime with a.

⇒So, a and b will be coprime as well as a and c will be coprime.

which proves that, a does not divide b.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

statement #3: proof- ang is congruent to ang ecd : angles are congruent.  

step-by-step explanation:

1: the missing angles in statement #3  

a.) acb  

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.  

2: the missing word in reason #3  

c.) vertical  

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.  

i hope that was and understanding.