Question

Which is a counterexample that disproves the conjecture?



For all real numbers n, |n| > 0.









A.

n = –0.5








B.

n = 0








C.

n = 0.5








D.

n = 3

Answer 1

HINT: What is \(|0|\)?

Answer 2

the absolute value of 0 right?

Answer 3

Yeah, and it equals to what?

Answer 4

0?

Answer 5

Right, so at n=0, we have \(|0| = 0\)

Here, is it true that \(0>0\)?

Answer 6

no, because its equal

Answer 7

Right, so \(n=0\) is counterexample here.

Answer 8

ohh thank you. can you please help me with 4 more?

Answer 9

Sure

Answer 10

Choose the counterexample that disproves the conjecture.



If n is a two-digit prime number, then the two digits must be different.









A.

n = 22








B.

n = 17








C.

n = 11








D.

n = 10

Answer 11

To find counterexample, we must find prime with two same digits.

Answer 12

So it's either A or C.

Answer 13

Which A or C is prime number? @harmony_coker

Answer 14

C

Answer 15

Right. Makes sense so far?

Answer 16

Yes.

Answer 17

Which is a counterexample that disproves the conjecture?



A student concludes that if x is a real number, then x ≥ x3.









A.



x = 3









B.

x = 1








C.

x = 0








D.

x = –1

Answer 18

You mean \(x\ge x^3\)?

Well, try plug in value of x then check whether it is true or not.

Let's start with x= 3.

Is it true that \(3\ge3^3\)?

Answer 19

\(3^3 = 3\times3\times3 = 27\)

So we have \(3\ge27\)

Answer 20

yes. so the answer would be 3?

Answer 21

Yes? 3 is greater than 27?

Answer 22

no 3 is less than 27

Answer 23

Right. \(3\ge27\) is false.

So we found counterexample. So x=3 is our answer.

Answer 24

thank you

Answer 25

Which is a counterexample that disproves the conjecture?



A student concludes that if x is a real number, then x^2 ≤ x^4.









A. 0


B. 1/4


C. 1



D. 5/4