Can it even be solved?
We can solve this problem in many ways, a truth table, or a logic tree. The latter seems more convenient, so it will be used.
First let's use some definitions of symbols.
For the names,
For the locations,
Now the operators:
K=L means Kay was discovered in the library (etc.)
K≠L means Kay was not discovered in the library.
-> means "then", or "it follows".
&xor; means exclusive or, exactly one of the two statements is true.
In logic, if the condition of a conditional statement is true, "it follows" that the following statement
is true. If the condition is NOT satisfied, we do not know if the following statement is true or not, i.e.
if a is true, we know that b is true
if a is not true, we don't know if b is true.
"If it rains, I stay home."
If it doesn't rain, I may stay home, or I may go out.
Now let's get started.
We will translate the four given statements:
1. K≠L ->A=A
2. B=L &xor; M=S
3. A=A -> M=S
4. B≠L -> K≠L
We have two cases, either (A) K was found in the Library, or (B) she was not.
A=A (from 1.)
B≠L (since K=L)
But from 4, B≠L -> K≠L
Contradiction, therefore K≠L
A=A (from 1, K≠L -> A=A)
M=S (from 3 A=A -> M=S)
(if(B≠L, then K≠L, then nobody was found in the library; => B=L)
K=C (by elimination)
If you have been following the logic, you would be able to translate the conclusion.
Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of an improper fraction.
3y + 5 >10
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