Question
Use De Morgan's law to write the negation of the followingstatements and simplify it 8<10 or 5 not equal to 2
Use De Morgan's law to write the negation of the following statements and simplify it 8<10 or 5 not equal to 2
Answers
Express the negation of each of these statements in terms of quantifiers without using the negation symbol. a) $\forall x(-2<x<3)$ b) $\forall x(0 \leq x<5)$ c) $\exists x(-4 \leq x \leq 1)$ d) $\exists x(-5<x<-1)$
Okay, so we want the negation of the following in quality, and so that's not. Q is greater than or equal to five, which must be Q is less than five.
We want to show that the converse of this statement is false. So we have. If eggs is equal to negative five, then the square root of X equals 25. So it's Converse would be flipped, saying that if X squared is equal to 25 then X equals negative five. Well, this is false because X could also equal just five. So because five times five is 25 but negative times negative five is also 25.
So this question we're asked whether the left hand side of the equation is equal or not equal to the right hand side of the equation. So let's evaluate this. So we know aid to the power off R to the power to It's actually a to the power off who are, and we see that's not equals to a to the power of our square. That's not equal because of this reason.
In this problem. We want to see if this is a true statement or not, and if it's not true, we need to make a true statement out of it. So let's check it out and see what we get. We want to see a five to the negative. Second power is greater than two to the negative fifth power. Well, let's find the values of both sides. Five to the negative Second power be rewritten as 1/5 to the second power and to the negative fifth Park be rewritten as one over to the fifth. Power 1/5 to the second. Power is five times five is 1/25 and to to the fifth, power is 32. So this will be 1/32. One divided by 25 is 250.4 and one divided by 32 is 0.3 So one 25th is greater than 1 30 seconds. So this is a true statement
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