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Chapter 3: Q12. (page 107)

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

Expert verified

From statements 鈥淧olygon G has more than 6 sides鈥� and 鈥淧olygon G has fewer than 8 sides鈥漜onclusion is that Polygon G has more than 6 sides and fewer than 8 sides.

Step by step solution

01

Step 1. Define deductive reasoning.

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

02

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 鈥�(颈)

As polygon G has fewer than 8 sides,

n<8 鈥�(颈颈)

03

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 鈥淧olygon G has more than 6 sides鈥� and 鈥淧olygon G has fewer than 8 sides鈥� conclusion is that Polygon G has more than 6 sides and fewer than 8 sides.

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