precedence rules, order of operations

[Fistandantilis]

This is a homework question, I just need a little help. I am doing truth tables for my descrete math class and I have to construct a truth table for a symbolic statement, I understand the order of operations but the statement I am stuck on has brackets ([]) and parentheses, here is the statement [~(p if r)] ^ q please I dont want the answer or the table that part I can figure out for my self but I dont know where the brackets stand in the order of operations. My book says to do parentheses first the negations, then conjuctions and then disjunctions. nothing about brackets.
any help would be nice, thanks

 

[Whitecloak]

[ > { > (

Do the innermost brackets first.

 

[xtknight]

I thought the braces came before the brackets as in { [ ( ?

 

[Fistandantilis]

Thanks Whitecloak, but what about what xtKnight said?

 

[xtknight]

As long as you follow the containers it should be fine, like:

{ 5+5 [ 5(5x-2)² ] }
[ 5+5 { 5(5x-2)² } ]

doesn't really matter.
do (5x-2)^2 first, then multiply by 5, then multiply by 10 (5+5) I think. 😱

 

[Fistandantilis]

crystal clear. thanks

 

[Fistandantilis]

OK, so I got a good grasp (I think) on constructing truth tables, but How do I find the truth value of a statement. Here is the question from my book 2 + 6 = 8 OR 7 - 12 = 5.
here is my truth table,
P = 2 + 6 = 8
Q = 7 - 12 = 5

P Q P or Q
T T T
T F T
F T T
F F F

So to find the truth value for P or Q, what do I do?
like I said in the OP dont tell me the answer I can figure that out by myself. I just need to know "how"

2 + 6 = 8 is true
7 - 12 = 5 is false
am I on the right track?

thanks

 

[DaveSimmons]

Yes, that looks right.

Perhaps another example will help:

P = cats chase mice
Q = cats like bubble baths

What is the truth of P AND Q ?

P Q P and Q
TT T
TF F
FT T
FF F

1. decide value of P ( = true)
2. decide value of Q ( = false)
3. read proper row of truth table = False (I've bolded the row)

 

[Fistandantilis]

Originally posted by: DaveSimmons
Yes, that looks right.

Perhaps another example will help:

P = cats chase mice
Q = cats like bubble baths

What is the truth of P AND Q ?

P Q P and Q
TT T
TF F
FT T
FF F

1. decide value of P ( = true)
2. decide value of Q ( = false)
3. read proper row of truth table = False (I've bolded the row)

OK, so because P= t and Q =F the line in the chart that has T F is the proper line to show the truth value?

thanks again