Question

Accept the two statements as given information. State a conclusion based on deductive reasoning. If no conclusion can be reached, write none.

Polygon G has more than 6 sides.

Polygon G has fewer than 8 sides.

Short answer

From statements “Polygon G has more than 6 sides” and “Polygon G has fewer than 8 sides”conclusion is that Polygon G has more than 6 sides and fewer than 8 sides.

Step-by-step solution

Step 1. Define deductive reasoning.

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Step 2. State the reasoning.

Let n denotes the number of sides of a polygon G.

As polygon G has more than 6 sides,

$n>6$ …(i)

As polygon G has fewer than 8 sides,

$n<8$ …(ii)

Step 3. State the conclusion.

From (i) and (ii),$6<n<8$.

In words, conclusion is that Polygon G has more than 6 sides and fewer than 8 sides.

Therefore, from statements “Polygon G has more than 6 sides” and “Polygon G has fewer than 8 sides” conclusion is that Polygon G has more than 6 sides and fewer than 8 sides.