Consider the following statement If a rook is bleen then for

Consider the following statement: If a rook is bleen, then for all grudzals there is a bleen mumrath that is on the rook. Let R be the set of rooks, G be the set of grudzals, M be the set of mumraths, B(x) represent \"x is bleen.\" and O(x, y) represent \"x is on the y.\" Write the statement in predicate logic. Formally negate the statement. Simplify your negation so that no quantifier lies within the scope of the negation. W rite an English translation of your negated statement.

Solution

R is the set of rooks.

If a rook is bleen, means B(x) is true

Hence in logic it says

B(x) implies O(x,y)

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Negation of statement is

B(x) does not imply O(x,y)

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If a rook is not bleen, then for all grudzals there is a bleen mumrath that is on the rook.