Click and drag the given steps (in the right) to their corresponding step names

Question

Click and drag the given steps (in the right) to their corresponding step names (in the left) to prove that if a|b and b|c, then a|c. Step1 Step 2 Step 3 Suppose alb and b|c. By definition of divisibility, a|b means that a = bt for some integer t, and b|c means that b = cs for some integer s. We substitute the equation b = at into c = bs and get c = ats. By definition of divisibility, a = c(st), with ts being an integer, implies a|c. By definition of divisibility, c = a(ts), with ts being an integer, implies a|c. Suppose a|b and b|c. By definition of divisibility, a|b means that b = at for some integer t, and b|c means that c = bs for some integers. We substitute the equation b = cs into a = bt and get a = cst.

Explanation / Answer

Lets suppose the options on right are numbered 1 to 6. So below are the steps

Step 1. - > Option 1 -- a/b = > a=bt

b/c => b =cs

Step 2) -> Option 6.

substitude b = cs in a =bt

a = cst

Step 3) Option 3 -

a = c(st)

st is an integer. So a/c hence proved.

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