basket of orange and apples?

Question

Here is a statement on logical reasoning :

some baskets have oranges . some baskets have apples . baskets have either apples or oranges .


is it true ?

please explain ..how do i come to a conclusion . its confusing

Answer 1

Strictly speaking, it is not true because there could be a basket consisting entirely of pears--this is not precluded by the first two statements.

Answer 2

Simple ... Use a Pie Diagram ...

Imagine Baskets and oranges and Apples as 3 different circles or Pies .

First - Some baskets have Oranges - Meaning a small portion of Baskets has oranges ... (The Basket and Orange Circles intersect but do not coincide.)

Second - Some baskets have Apples - Same as the above ... However The baskets and apples circles might intersect at a different point ... (meaning Oranges and Apples may or may not intersect)

Hence - Baskets have either apples or Oranges - (False) Baskets might have both apples and oranges .

Answer 3

No it's not
.A proof can be given by using a simple counter-example:
Take three baskets and name them b1,b2 and b3.
Put two apples and three oranges in b1.
Put four oranges in b2.
Leave b3 empty ( or you can put some bananas,mangos
and a water melon if you like!)

In this case,some baskets do have apples (b1),some baskets do have oranges (b1,b2) but a basket need not to have either apples or oranges (b1 have them both and b3 have neither).

Using diagrams is fine and in general logical problems is the usual approach,but that's also the case with counter-examples,so in every way we have a strict 'proof'...

Answer 4

Not necesarily. If some baskets have oranges and some have apples, it does not mean all baskets have either apples or oranges. Some baskets may have something else, or be empty

Answer 5

I think you need a phrase like "some baskets" or "all baskets contain apples or oranges" to decide if this is true or not. What if there are other baskets containing peaches for example?