sole2 - ANALYSIS EXERCISE 2SOLUTIONS 1. (a) (x (Ac )c ) (x...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ANALYSIS EXERCISE 2–SOLUTIONS 1. (a) ( x ( A c ) c ) ⇔ ¬ ( x A c ) ⇔ ¬¬ ( x A ) ( x A ). (b) ( x ( A B ) c ) ⇔ ¬ ( x ( A B )) ⇔ ¬ ( x A ) ( x B ) [ ¬ ( x A ) ∧ ¬ ( x B )] [( x A c ) ( x B c )] ( x A c B c ) . (c) ( x ( A B ) c ) ⇔ ¬ ( x ( A B )) ⇔ ¬ ( x A ) ( x B ) [ ¬ ( x A ) ∨ ¬ ( x B )] [( x A c ) ( x B c )] ( x A c B c ) . 2. (a) ( x A 4 B ) ⇔ { [( x A ) ∧ ¬ ( x B )] [( x B ) ∧ ¬ ( x A )] } ⇔ { [( x A ) ( x B )] [( x A ) ∨ ¬ ( x A )] [ ¬ ( x B ) ( x B )] [ ¬ ( x B ) ∨ ¬ ( x A )] } ⇔ { [( x A ) ( x B )] [ ¬ ( x B ) ∨ ¬ ( x A )] } ⇔ { [( x A ) ( x B )] ∧ ¬ [( x B ) ( x A )] } ⇔ { ( x A B ) ∧ ¬ ( x A B ) } . (b) From (a) it follows that (0.1) ( A 4 B = ) [( A - B = ) ( B - A = )] . Now let us prove that
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/25/2010 for the course MATHEMATIC 11007 taught by Professor Spyros during the Winter '10 term at Bristol Community College.

Page1 / 3

sole2 - ANALYSIS EXERCISE 2SOLUTIONS 1. (a) (x (Ac )c ) (x...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online