Discrete Structure Math **3. Write the contrapositive of:**For all $ a \in \mathbb{Z} $, if $ 6 \mid a $ then $ 2 \mid a $ and $ 3 \mid a $.**4. Write negations of the following quantified statements:**(a) For all $ x \in \mathbb{R} $, if $ |x| > 5 $ then $ x < -5 $ or $ x > 5 $.(b) There exist $ a, b \in \mathbb{Z} $, such that $ a \mid b $ and $ b \mid a $.**5. The following statement is false, write the negation and disprove it using a counterexample:**For all $ x \in \mathbb{R} $, if $ x < 2 $ then $ x^2 < 4 $.

Name: Discrete Structure Math **3. Write the contrapositive of:**For all $
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Description: Discrete Structure Math **3. Write the contrapositive of:**For all \( a \in \mathbb{Z} $, if $ 6 \mid a $ then $ 2 \mid a $ and $ 3 \mid a $.**4. Write negations of the following quantified statements:**(a) For all $ x \in \mathbb{R} $, if \

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Discrete Structure Math

**3. Write the contrapositive of:**

For all $ a \in \mathbb{Z} $, if $ 6 \mid a $ then $ 2 \mid a $ and $ 3 \mid a $.

**4. Write negations of the following quantified statements:**

(a) For all $ x \in \mathbb{R} $, if $ |x| > 5 $ then $ x < -5 $ or $ x > 5 $.

(b) There exist $ a, b \in \mathbb{Z} $, such that $ a \mid b $ and $ b \mid a $.

**5. The following statement is false, write the negation and disprove it using a counterexample:**

For all $ x \in \mathbb{R} $, if $ x < 2 $ then $ x^2 < 4 $.

Expert Solution

Step 1

We are given a conditional statement as-

“If p then q.”

A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.

The contrapositive of such statements is written as-

“If not q then not p.”

Also we can say that if the statement is true, then the contrapositive is also logically true. .

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