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A' is the set of all triangles with all angles 60°.

how

A is the set of all triangles with at least one different angle from 60°.

So that means that A' is the set of all equilateral triangles.

lol u wrote the same thing

i neeed A compliment

\(\Huge A'\)

Jesus. I just typed everything out and it removed it.

OK, so \(A'\) *is* the set of equilateral triangles.

type it on notepad first then copy

Or you could use a better site such as www.peeranswer.com

no i have faith in OP.com

Read that as "I have faith in OP's mom"

OP.com??????

OPenstudy.com

ohhhhh :O

lol

hmm this is confujing

whats the negation of below statement :
at least of the gifts is a car

car is not in the gifts

right, another
whats the negation of below statement :
at least of the gifts is not a car

Their might be car as gift more than once.

try again

at least of the gifts is a car

```
at least of the gifts is not a car
```
means, there exist one or more gifts that are not cars

whats the negation of that ?

this_>? at least of the gifts is a car

nope

negation of "at least one" is "none"

i mean negation of which sentence

ok i see my english is poor

it has nothing to do with english, it is logic, you just need to see it once

may be lets work this with venn diagrams

|dw:1438798363617:dw|

Yes, that looks good. can you show me A and A' in above venn diagram

|dw:1438798432076:dw|

as expected, you can see that combining A and A' covers the entire U

ok

what about \(A\cap A'\) ?
is there anything common between A and A' ?

nothing common

since there is nothing common, we say it equals `emptyset`, \(\varphi\)

\[A\cap A' = \varphi\]

ok

this one \(\emptyset′ ∩ A\) =

whats the compliment of emptyset ?

make a guess

\( \emptyset\)

try again

by definition, complement is different from the original

emptyset and universal set are complements of each other

\(\varphi' = U\)
\(U' = \varphi\)

ok i see

so \(\emptyset′ ∩ A=U\cap A = ?\)

Yep, try the last one

\[\emptyset\]

Yes \(U′ ∩ A = \varphi \cap A = \varphi\)

thnx