PROBLEM 3 The domain of discourse for this problem is a group of three people who are working on a project. To make notation easier, the people are numbered 1, 2, 3. The predicate M(r, y) indicates whether x has sent an email to y, so M(2, 3) is read "Person 2 has sent an email to person 3." The table below shows the value of the predicate M(z, y) for each (r, y) pair. The truth value in row z and column y gives the truth value for M(r, y). M| 1|2 1 T. T. 2 T. T|F Determine if the quantified statement is true or false. Justify your an- swer. (a) Vz Vy (z + y) → M(r, y)) (b) Vz 3y -M(z, y) (c) 3r Vy M(r, y)

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PROBLEM 3
The domain of discourse for this problem is a group of three people who are
working on a project. To make notation easier, the people are numbered 1, 2, 3.
The predicate M(x, y) indicates whether x has sent an email to y, so M(2, 3) is
read "Person 2 has sent an email to person 3." The table below shows the value of
the predicate M(x, y) for each (r, y) pair. The truth value in row r and column
y gives the truth value for M(r, y).
12 3
1
T.
T.
TF|T
TT
F
Determine if the quantified statement is true or false. Justify your an-
swer.
(a) Vz Vy (z + y) → M(z, y))
(b) Vr 3y -M(r, y)
(c) ar Vy M(r, y)
2/3
Transcribed Image Text:PROBLEM 3 The domain of discourse for this problem is a group of three people who are working on a project. To make notation easier, the people are numbered 1, 2, 3. The predicate M(x, y) indicates whether x has sent an email to y, so M(2, 3) is read "Person 2 has sent an email to person 3." The table below shows the value of the predicate M(x, y) for each (r, y) pair. The truth value in row r and column y gives the truth value for M(r, y). 12 3 1 T. T. TF|T TT F Determine if the quantified statement is true or false. Justify your an- swer. (a) Vz Vy (z + y) → M(z, y)) (b) Vr 3y -M(r, y) (c) ar Vy M(r, y) 2/3
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