Simplify the following symbolic statements as much as you can, leaving your answer in a standard symbolic form. Express each of your answers in natural English.
You are right on a--I missed that. You can certainly learn to think in truth tables. Learning gets slower as we get older, but it still happens with work.
(a) inside the parentheses, it says pi is greater than 3.2. Outside is the "not" symbol. The final sentence is "Pi is not greater than 3.2". This is a true statement.
(b) not "x is less than 0" means "X is greater than 0. Thus, x is any positive number greater than 0.
(c) x^2 is greater than 0 for any number except 0. not x^2 > 0 means that x^2 is less than or equal to zero. The only solution for this is x = 0.
(d) not x = 1 means that x = any number except 1.
(e) the two nots "undo" each other. this is the same as phi.
You are right, Margie. Been too many years since I was in a math classroom. Even when I taught, I would tell my students that they should not expect more than 95% of my answers would be right. Gave them incentive to think and reason when my answer was wrong!
a) π < 3.2
ReplyDeleteb) x ≥0
c) x=0
d) x ≠ 1
e) ψ
These are hard for me. I agree with you on b, d and e, but I'm thinking of these for the others:
Deletea) π ≤ 3.2
c) x² ≤ 0
Please excuse the mis-post previously sent as a comment
I agree with you on a, but I think that c has to be x squared = 0 because if you take the square root of x, it can't be negative, right?
ReplyDeleteThat's true, Sarah. ;-)
DeleteMaybe my brain will learn to think in truth tables. Margie and Diane, what do you think?
You are right on a--I missed that.
DeleteYou can certainly learn to think in truth tables. Learning gets slower as we get older, but it still happens with work.
Yes, Francis, you can learn. You just have to WANT to learn, first. :)
ReplyDeleteNow, my solutions to these:
ReplyDelete(a) inside the parentheses, it says pi is greater than 3.2. Outside is the "not" symbol. The final sentence is "Pi is not greater than 3.2". This is a true statement.
(b) not "x is less than 0" means "X is greater than 0. Thus, x is any positive number greater than 0.
(c) x^2 is greater than 0 for any number except 0. not x^2 > 0 means that x^2 is less than or equal to zero. The only solution for this is x = 0.
(d) not x = 1 means that x = any number except 1.
(e) the two nots "undo" each other. this is the same as phi.
(b) it seems to me that x =0 is also true.
DeleteYou are right, Margie. Been too many years since I was in a math classroom. Even when I taught, I would tell my students that they should not expect more than 95% of my answers would be right. Gave them incentive to think and reason when my answer was wrong!
Delete