SOLUTION: Given p is false, q is true, and r is true, find the truth value of the statement (p ~q) &#8596; ~r. Show step by step work. Use keyboard shortcuts of --> for , <--> for &#859

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Given p is false, q is true, and r is true, find the truth value of the statement (p ~q) &#8596; ~r. Show step by step work. Use keyboard shortcuts of --> for , <--> for &#859      Log On


   

Question 466866: Given p is false, q is true, and r is true, find the truth value of the statement (p ~q) ↔ ~r.
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Answer by Big Poop(157) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-2x%2B-3 can be factored:
1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29
Again, the answer is: 3, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-3+%29
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