Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Discrete Structure Math
Transcribed Image Text:**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
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Step 1
3)
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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