arifaisal wrote:

wilbur is over six feet tall. the statement above can be logically deduced from which of the following statements?

a)the average height of the members of the basketball team is over six feet; wilbur is the center on the basketball team.

b)if wilbur was not asked to join the cricket team, then he is not six feet tall; wilbur was asked to join the cricket team.

c)if wilbur is over six feet tall, then he can see the parade; wilbur can see the parade.

d)in dr. gray's seminar, everyone who is not over six feel tall is seated in the first row; dr. gray seated wilbur in the second row.

e) everyone who is over six feet tall has to help stack cartons in the stockroom; wilbur has to help stack cartons.

Answer d.

We want to logically deduce the following: Wilbur is over 6' tall.

This means, we want to prove beyond a doubt that Wilbur is over 6' tall. To rephrase it, we want to say that it [highlight]must be true[/highlight] that Wilbur is over 6' tall.

a) the average height of the members of the basketball team is over six feet; wilbur is the center on the basketball team.

All we can say is that the average height is over 6'. It is possible that 2 people are 7' tall and the rest are all less than 6'. Whether Wilbur is more than 6', we cannot say for sure.

b) if wilbur was not asked to join the cricket team, then he is not six feet tall; wilbur was asked to join the cricket team.

Something about conditionals here: Given -> If A, then B

The only 2 things it implies are:

1. If A is given to be true, B has to be true. (A -> B) A implies B

2. If not B (negative of B) is given to be true, not A is true. (B' -> A') Negative of B implies negative of A.

No other relation is implied.

e.g. If it rains, the grounds get wet.

If I know that it has rained, I can say that the grounds must be wet.

If I know that the grounds are not wet, it means that it did not rain.

But if I say that it did not rain, can I say that the grounds did not get wet? No because perhaps someone turned on the sprinklers or something... My statement does not imply that the ground cannot get wet in any other way. All it says is that it rains, then the ground certainly gets wet.

On those lines, this statement is similar to 'If A then B.'

We have been given A'. It doesn't imply anything about B.

c) if wilbur is over six feet tall, then he can see the parade; wilbur can see the parade.

Again, this is of the form If A then B.

We have been given B. It doesn't imply anything about A.

d) in dr. gray's seminar, everyone who is not over six feel tall is seated in the first row; dr. gray seated wilbur in the second row.

Everyone not over 6' is seated in the first row i.e. everyone who is 6' or less is seated in the first row. If Wilbur were 6' or less, he would be seated in the first row. Since he is not seated in the first row, he must not be 6' or less i.e. he must be over 6'.

or

This can be converted to 'If then' format.

If one is not over 6', he/she is seated in the first row.

We have been given B' (negative B). This implies negative A i.e. Wilbur is over 6'.

Answer.

e) everyone who is over six feet tall has to help stack cartons in the stockroom; wilbur has to help stack cartons.

If one is over 6', he has to help stack cartons.

We have been given B (he has to help stack cartons). B does not imply anything about A.

It is possible that some people who are not over 6' are also required to help.

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Karishma

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