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CMSC 150 INTRODUCTION TO DISCRETE MATH HOMEWORK 6

CMSC 150 INTRODUCTION TO DISCRETE MATH HOMEWORK 6

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The total number of points is 10. Your total score will be divided by 10 to produce a score over 100. Show all workunless checkboxes are provided.1Using the predicate symbols shown and appropriate quantifiers, write each English language statement in predicatelogic. The domain is the whole world. In the definition of a predicate, the variables are placeholders. They will getinstantiated within the scope of the quantifiers. 3 points (1 point each)P(x) is ”x is a person.”T(x) is ”x is a time.”F(x,y) is ”x is fooled at y.”1. You can fool some of the people all of the time.2. You can fool all of the people some of the time.3. You can’t fool all of the people all of the time.2Which of the following is the correct negation for “Nobody is perfect.”(1 point) Check only one11. Everyone is imperfect.2. Everyone is perfect.3. Someone is perfect.3Write the negation of each of the following with a positive statement (in English):3 points (1 point each)1. Some farmer grows only corn.2. Some farmer does not grow corn.3. Corn is grown only by farmers.4Write the negation of the following quantified statement. Move the negation symbol as far inside the predicate aspossible. Assume that x, y, and z are all in the universe U. (1 point)∃x∀y∀z[(F(x, y)∧G(x,z)) → H(y,z)]5Prove that the expression below is a valid argument using the deduction method (that is using equivalences and rulesof inference in a proof sequence) (2 points)(∃x)[P(x) → Q(x)]∧(∀y)[Q(y) → R(y)]∧(∀x)P(x) → (∃x)R(x)


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