“All birds have wings but some birds cannot fly.” Question #1 Write this stateme

Question

“All birds have wings but some birds cannot fly.”

Question #1

Write this statement symbolically as a conjunction of two sub-statements, one of which is a conditional and the other is the negation of a conditional.

Use three components (p, q, and r) and explicitly state what these components correspond to in the original statement.

Hint: Any statement in the form "some X cannot Y" can be rewritten equivalently as “not all X can Y,” or "it is not the case that X can Y." Here X denotes a class of objects and Y denotes a specific property pertaining to these objects.

Explanation / Answer

First, define three statements (about the item/animal being considered)

p = it is a bird
q = it has wings
r = it can fly

Statement #1 (S 1)

p ===>> q "If it's a bird, then it has wings"

(i.e. birds have wings)

Statement #2 (S2)

p =//=>> r " something being a bird DOES NOT imply that it can fly"

(i.e. birds are not necessarily capable of flying)

the CONJUNCTION of these statements ( S1 AND S2) is as follows:

[ p ==> q ] ^ [ p =/= > r ]

( i.e. birds have wings but birds are not necessarily able to fly )

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