Question

I need help with this algebra 2 question? It's in the comments.

Answer 1

Give an example of a conjunction that is used in the real world. Then, give another example of a disjunction that is used in the real world. Explain clearly why each example is either a conjunction or a disjunction. Then describe what the graph and interval notation for each would look like.

Answer 2

(Please don't tell me this is in the wrong subject because I will screenshot this exact question in my math course and post it if I must)

Answer 3

a conjunction example:
to vote you need to be 18+ and a citizen of the united states . (either condition alone is not enough, you need both)

Answer 4

oh you want an algebra problem that uses conjunction

Answer 5

I think that I understand the conjunction/disjunction part - just any real world example of something with and and or. But what is confusing me is how to describe the graph and interval notation.

Answer 6

conjunctions come up when we solve abolsute value inequalities
For example if I say
"Suitable temperature to operate this machine is within 50 degrees of zero degrees celsius"

Answer 7

Conjunction: They smiled and laughed (they did both things)
Disjunction: They either smiled or laughed (one or other)

Graph would be a Venn diagram with 2 circles. Where they overlap is a conjunction, the rest of the area covered by both circles are your disjunctions, outside the circles and inside the bounding square is the rest of language!

Interval notation: conjunction<disjunction<language

Answer 8

in other worlds
A "logical disjunction" simply means : " or " so;
"A ∨ B " is read as "A or B ". Such a disjunction is false if both A and B are false.
So, the result would be true if one or more operands are true.
It would only be false if both or all it's operands are false.

A "logical conjunction" simply means "and" so;
the symbol is an inverted "v"
" A (inverted v) B " are read as " A and B " . The conjunction would only be true if and only if both operands are true, otherwise it would be false.

okay:
properties under the conjunctions are:

1. "Associativity": the order of operations does not matter as long as the sequence of the operands is not changed. Eventhough parenthesis are changed, operands will still act the same.
ex: (5+1) +5 = 5+ (1+5)

2. "Commutativity": to the ability to change the order of something without changing the end result.
ex: 3 + 5 = 5 + 3 for addition; 5*3 = 3*5 for multiplication

3. "Distributivity": uses the "dristibutive law"
ex: 5( 2 + 3) = (5*2) + (5*3)

4. "Idempotence": multiple applications of that operation will yield the same result.
unary operations:
- the absolute value operation is a unary operation on the real numbers
- the opposite operation (-x) on the real numbers
- the power operations (squaring, cubing, etc) on the real numbers
- the factorial operation on the real numbers
- the trigonometric functions (sin x, cos x, tan x, cot x, csc x, sec x) on the real numbers
- the natural logarithm (ln x) on the real numbers
- the logarithm of base 10 (log x) on the real numbers
- logical negation on truth values

These are examples of unary operations, and could be subject to "Idempotence"

5. "Monotonic" - actually these are used mostly for calculus..

There's much more to explain, but it would be best if there would be an example for it? have a nice day!

Answer 9

@ChiefArnav Those are copied answers from yahoo answers..they didn't help me at all with this problem which is why I'm here :)

Answer 10

example of conjunction:
"To compete at wrestling in lightweight division an athlete must weight at least 90 pounds and no more than 130 pounds. "
I am guessing on those figures, we can look them up on wikipedia

Answer 11

these two sentences can be represented algebraically by
w>= 90 and w <= 130 , where w = weight in pounds

Answer 12

So if I were to describe the graph of that, I would say there would be a closed dot on 90 and a closed dot on 130 and it would be filled in in between? Meaning everything including and between 90 and 130 is a solution?

Answer 13

right

Answer 14

w >= 90
[======>

w <= 130
<============= ]

where they overlap is the compound solution
90 <= w <= 130

Answer 15

And for a disjunction, I could say (sticking with the wrestling example for the sake of this thread) to compete in junior wrestling, an athlete must be below/exactly 13 or to compete in senior an athlete must be above/exactly 14? So the graph would be a closed dot on 13 and all the numbers to the left and a closed dot on 14 and all the numbers to the right?

Answer 16

I was thinking of this example.
in a certain lake, anglers may keep fish that are less than 15 inches long and fish that are greater than 25 inches long

Answer 17

let L be the length of the fish.
this produces two inequalities
L < 15 or L > 25

Answer 18

this is an example of a disjunction

Answer 19

you can be more detailed about the type of fish, walleyes lets say

Answer 20

or maybe bass :)

Answer 21

Ah okay, I think I get it now. Thank you! My main issue was how to describe the graphs and interval notations but I understand now :) @perl