Which of the following sentences is logically equivalent to -Vy(P(r, y) → Q(z, y))?O arVy(P(r, y) A-Q(2, y))Elarvy(-Q(z, y) → -P(z, y))O Valy(P(z, y) A¬Q(z,y))Vzay(-Q(r,y) P(z, y))Consider the sentences ValyP(z, y) and 3yVa P(r, y). Are these sentences true or false under the interpretation where z and y rangeover the positive integers and P(r, y) is 'y 2 3z?VayP(z, y) is true, JyvzP(z, y) is trueO VzayP(z, y) is true, 3yvrP(r, y) is falseO VzayP(z, y) is false, yvzP(z,y) is trueO ValyP(z, y) is false, 3yvaP(r, y) is falseConsider the sentences ValyP(z,y) and yvzP(z, y). Are these sentences true or false under the interpretation where z and y rangeover the integers and P(z,y) is "a = 5y?o ValyP(z, y) is true, JyVa P(r, y) is trueO VzyP(z, y) is true, JyvrP(1, y) is falsee VayP(z, y) is false, yvaP(z, y) is trueVayP(z, y) is false, yvaP(z, y) is falseConsider the sentence CzP(z) A zQ(z)) - J(P(z) A Q(x)) Which of the following is true?A. The sentence is valid.B. The sentence is not valid. It is false under the interpretation where z ranges over the positive integers, P(z) is "z <3 and Q(x)is "z> 6".OC. The sentence is not valid. It is false under the interpretation where a ranges over the positive integers, P(z) is 'z>3' and Q(=)is z> 6.OD The sentence is not valid. It is false under the interpretation where a ranges over the positive integers, P(2) is "<-3" andQ(z) is "z > 6".

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Description: Which of the following sentences is logically equivalent to -Vy(P(r, y) → Q(z, y))?O arVy(P(r, y) A-Q(2, y))Elarvy(-Q(z, y) → -P(z, y))O Valy(P(z, y) A¬Q(z,y))Vzay(-Q(r,y) P(z, y))Consider the sentences ValyP(z, y) and 3yVa P(r, y). Are these senten

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Which of the following sentences is logically equivalent to -JarVy(P(z, y)- Q(, y))? O BarVy(P(r, y) A-Q(a,y)) O arVy(-Q(z,y)→-P(z,y)) O Va3y(P(r,y) A¬Q(z,y)) Vaay(-Q(z,y)¬P(x, y))

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Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Which of the following sentences is logically equivalent to -Vy(P(r, y) → Q(z, y))?
O arVy(P(r, y) A-Q(2, y))
Elarvy(-Q(z, y) → -P(z, y))
O Valy(P(z, y) A¬Q(z,y))
Vzay(-Q(r,y) P(z, y))
Consider the sentences ValyP(z, y) and 3yVa P(r, y). Are these sentences true or false under the interpretation where z and y range
over the positive integers and P(r, y) is 'y 2 3z?
VayP(z, y) is true, JyvzP(z, y) is true
O VzayP(z, y) is true, 3yvrP(r, y) is false
O VzayP(z, y) is false, yvzP(z,y) is true
O ValyP(z, y) is false, 3yvaP(r, y) is false
Consider the sentences ValyP(z,y) and yvzP(z, y). Are these sentences true or false under the interpretation where z and y range
over the integers and P(z,y) is "a = 5y?
o ValyP(z, y) is true, JyVa P(r, y) is true
O VzyP(z, y) is true, JyvrP(1, y) is false
e VayP(z, y) is false, yvaP(z, y) is true
VayP(z, y) is false, yvaP(z, y) is false
Consider the sentence CzP(z) A zQ(z)) - J(P(z) A Q(x)) Which of the following is true?
A. The sentence is valid.
B. The sentence is not valid. It is false under the interpretation where z ranges over the positive integers, P(z) is "z <3 and Q(x)
is "z> 6".
OC. The sentence is not valid. It is false under the interpretation where a ranges over the positive integers, P(z) is 'z>3' and Q(=)
is z> 6.
OD The sentence is not valid. It is false under the interpretation where a ranges over the positive integers, P(2) is "<-3" and
Q(z) is "z > 6".

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