1. Convert the following statement to a quantified expression, negate it, and convert the answer back to English. You will end up with the exact opposite concept.
All cats are asleep.
2. Convert the following statement into a quantified expression:
Everyone, who has seen Deadpool, likes chimichangas .
3. Simplify the following Quantified Statement. The result should have no negation symbols. ¬ ?x ?x (¬G(x) ? H(x) )
4. Prove the following using induction (show your work- both steps):
If x?2then2+4+6+...+2n = n(n+1)
SOLUTION TO QUESTION 1:
Let C(x) denote that x is a cat and S(x) denote that x is asleep.
Hence, ALL CATS ARE ASLEEP can be written as:
The negation of this statement is given as
which is equivalemnt to
which can be interpreted as -
There exists an element x for which x is asleep does not hold. In other words, there is at least a cat which is not asleep.
SOLUTION TO PROBLEM 2:
Everyone, who has seen Deadpool, likes chimichangas.
Assume that D(x) means that x has seen Deadpool and C(x) implies that x like chimichangas. Thus, the above statement can be re-written in quantifier form as:
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The problem 3 and 4 are beyond understanding. I guess the question replaces some important quantifier/implication condition with ? sign which cannot be interpreted here. I will advise you to re-post these questions with correct conditions.
1. Convert the following statement to a quantified expression, negate it, and convert the answer back...
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