Question

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 (x, y) pair. The truth value in row x and column y gives the truth value for M(x, y). | | 1 | 2 | 3 | |---|---|---|---| | 1 | T | T | T | | 2 | T | F | T | | 3 | T | T | F | Determine if the quantified statement is true or false. Justify your answer. (a) $\forall x \forall y ((x \neq y) \rightarrow M(x, y))$ (b) $\forall x \exists y \neg M(x, y)$ (c) $\exists x \forall y M(x, y)$

          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 (x, y) pair. The truth value in row x and column y gives the truth value for M(x, y).

|   | 1 | 2 | 3 |
|---|---|---|---|
| 1 | T | T | T |
| 2 | T | F | T |
| 3 | T | T | F |

Determine if the quantified statement is true or false. Justify your answer.
(a) $\forall x \forall y ((x \neq y) \rightarrow M(x, y))$
(b) $\forall x \exists y \neg M(x, y)$
(c) $\exists x \forall y M(x, y)$

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 mx y indicates 38113

Added by Suzanne A.

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