Condition/Truth Table

melwin · #1 $Old$ October 29th, 2009, 04:07 PM

Does anybody have any idea about this stuff?
Are the 2 conditions equivalent? Explain why.
a. Not(a<=b)
(a>=b) OR Not (a=b)

b. Not(a<=b)
(a>=b) AND Not (a=b)

Write a condition equivalent to the negation of the given condition, and that does not use the NOT operator.
a. a<b

b. (a>b) And (c<>d)

c. (a=b) Or (a=c)

Soroban · #2 $Old$ October 30th, 2009, 12:55 PM

Hello, melwin!

Quote:

Are the 2 conditions equivalent? Explain why.

$\text{(a)}\;\text{ Not }(a \leq b)$

. . $(a \geq b)\text{ or Not } (a=b)$

$a \leq b$ means: $(a$ is less than $b)$ or ( $a$ equal to $b.)$

Its negation is: . $\sim(a \leq b) \quad=\quad\sim\bigg[(a\text{ is less than }b) \text{ or } (a = b)\bigg]$

By DeMorgan's Law, this is: . $\sim(a\text{ is less than }b)\:\text{ and }\sim(a - b)$

. . . . . . . . . . . . . . . . $=\;(a\text{ is greater than or equal to }b)\;\text{ and }\:(a \neq b)$

. . . . . . . . . . . . . . . . . . . . $=\;(a \geq b) \text{ {\color{red}and} Not }(a = b)$

This is not what the second statement says; they are not equivalent.

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