Basic logic and proofs

P : I am young

Q : I am happy

Write “I am old but happy” in symbolic form.

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Tags

CCSS.HSA.SSE.B.3

P : I am young

Q : I am happy

Write “I am happy if and only if I am young” in symbolic form.

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• If I am not happy then I am young

• I am happy and young

• I am young but happy

• If I am not young then I am not happy

Tags

CCSS.HSA.SSE.A.1

Choose the correct answer for the following truth table:

• T T T F

• F T T F

• T T T T

• T T F F

Choose the correct answer for the following truth table:

• T T T F

• T F T F

• T T T T

• T T F F

Write the output of the following logic circuit.

• AB + ((B + C) . BC))

• AB((B + C) + BC))

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Draw the logic circuit to implement the following Boolean Expression:

(A+B) (C+D)

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Let P(x) =x is pretty where x is the set of people. Express the following quantification in English.

• Not everyone is not pretty

• Someone is pretty

• Everyone is pretty

• Not everyone is pretty

Let P(x) =x is pretty where x is the set of people. Express the following quantification in English.

• Someone is pretty

• Not all is pretty

• Someone is not pretty

• Not someone is not pretty

Let P(x) be the predicate "x likes reading" and Q(x) be the predicate “x can speak French”. The domain for both predicates are lecturers in PBU . Use quantifiers and logical connectives to express each of the following statement.

“Every lecturer in PSIS likes reading if they cannot speak French”

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