Need Help Understanding Set Concepts Logic!

[PotatoesForBrains]

Hi guys!

So this problem is tripping me up and I'm sure it has a simple explanation, but;
1. Maybe it's the phrasing I'm having trouble with, but why would 19 be GREATER THAN when it clearly has a LESS THAN symbol after it?
2. Would it read like X is Less than 19 but Less than or equal to 22? (Even though that's a completely illogical statement?
Sorry if this is a completely stupid question, but I just can't figure out how having two less than symbols creates a greater than equation. Thank you for any help! <3

 

[lev888]

Hi guys!

So this problem is tripping me up and I'm sure it has a simple explanation, but;
1. Maybe it's the phrasing I'm having trouble with, but why would 19 be GREATER THAN when it clearly has a LESS THAN symbol after it?
2. Would it read like X is Less than 19 but Less than or equal to 22? (Even though that's a completely illogical statement?
Sorry if this is a completely stupid question, but I just can't figure out how having two less than symbols creates a greater than equation. Thank you for any help! <3

View attachment 28920

19 < x means x is greater than 19.

 

[pka]

Hi guys!

So this problem is tripping me up and I'm sure it has a simple explanation, but;
1. Maybe it's the phrasing I'm having trouble with, but why would 19 be GREATER THAN when it clearly has a LESS THAN symbol after it?
2. Would it read like X is Less than 19 but Less than or equal to 22? (Even though that's a completely illogical statement?
Sorry if this is a completely stupid question, but I just can't figure out how having two less than symbols creates a greater than equation. Thank you for any help! <3

View attachment 28920

To Potatoes, You could post what you think is(are) the correct answer(s). We could then comment thereby helping your understanding.

 

[PotatoesForBrains]

To Potatoes, You could post what you think is(are) the correct answer(s). We could then comment thereby helping your understanding.

Hi PKA!

So what's tripping me up is this;
19 < x means x is greater than 19. I think I can understand that (Even though to me it reads as 19 is LESS than X, but okay). But how do I read it when 19 < x ≤ 22?

19 is greater than x, and x is greater than or equal to 22?

 

[Dr.Peterson]

Hi guys!

So this problem is tripping me up and I'm sure it has a simple explanation, but;
1. Maybe it's the phrasing I'm having trouble with, but why would 19 be GREATER THAN when it clearly has a LESS THAN symbol after it?
2. Would it read like X is Less than 19 but Less than or equal to 22? (Even though that's a completely illogical statement?
Sorry if this is a completely stupid question, but I just can't figure out how having two less than symbols creates a greater than equation. Thank you for any help! <3

View attachment 28920

The statement [imath]19<x\le 22[/imath] means [imath]19<x[/imath] and [imath]x\le 22[/imath]. In turn, [imath]19<x[/imath] means that 19 is less than x; if that is true, then x is greater than 19.

These symbols must be read from left to right; when you reverse the order of the numbers, you have to reverse the meaning of the relation. You can't read [imath]19<x[/imath] as "x is less than 19", as you are doing. In the same way, when you read "dog bites man", you can't take it to mean the man is doing the biting! Here, it's 19 that is less, not x.

 

[pka]

Hi PKA!
So what's tripping me up is this;
19 < x means x is greater than 19. I think I can understand that (Even though to me it reads as 19 is LESS than X, but okay). But how do I read it when 19 < x ≤ 22?
19 is greater than x, and x is greater than or equal to 22?

Just to add to Prof. Peterson's reply, it seems to me that you have miss out on some very basic vocabulary on inequalities.
[imath]19<n\le 20[/imath] is read as [imath]19[/imath] is less than [imath]n[/imath] which is less than or equal to [imath]20[/imath].
Do you understand that [imath]10\le x <12[/imath] is equivalent to [imath]12>x\ge 10~?[/imath] .

 

[PotatoesForBrains]

Thank you for all the feedback and help. I really appreciate it!

Okay, so:
19 is less than x
and x is less than or equal to 22.
Therefore; X is 20, 21, 22? (All natural numbers)
So the answer would be E?

 

[Steven G]

There is only one reason why 19< x (read as 19 is less than x) and that is because x > 19 (read as x is greater than 19)

I would read a < x < b as x is between a and b. That is more meaningful compared to a is less than x and x is less than b.

For example, 5 < x < 10 means that x is between 5 and 10. That is clear! x can be 7.5, sqrt(33), 8, 26/5, ... .

 

[Steven G]

But how do I read it when 19 < x ≤ 22?

x is between 19 and 22, x can NOT be 19 but can be 22

 

[JeffM]

Thank you for all the feedback and help. I really appreciate it!

Okay, so:
19 is less than x
and x is less than or equal to 22.
Therefore; X is 20, 21, 22? (All natural numbers)
So the answer would be E?

Yes.