Assignment 9 for COT3100

- (10) Draw a truth table for the compound statement .
- (15) Use the laws of logic to show that .
- (15) Show by any valid method except Venn diagram that .
- (35) Given the sets and :
- (5) Determine which one is a subset of the other.
- (20) Prove that subset property by universal generalization.
- (10) Prove by counter-example that they are
equal sets.*not*

- (25) Accepting the premises:

Conclude .

- (25) Prove by induction that for positive integers , .
- (15) Prove that if 7 divides with remainder 1, 7 divides with remainder 3.
- (20) Taking into account identical letters, how many ways are there to arrange the word PARVAMONSTRA that both begin and end with consonants?
- (15) How many unique combinations of monsters can a small monster collector capture, if that collector:
- Has 22 small monster containment devices
- Intends to use all of those devices
- Has access to Earth, Fire, Ice, and Steam type small monsters
- Intends to capture
*at least*three Ice,*at least*two Earth and*at most two*Steam type small monsters

**For questions 11 and 12, **a small monster collector has captured thirty-one Anachronism-type small monsters. Each Anachronism-type small monster has a 27% chance of being a Phlogiston-subtype and a 47% chance of being an Aether-subtype; it cannot be both.

- (5) What is the probability that exactly seven of the captured small monsters are Phlogiston-subtypes?
- (10) What is the probability of all but five of the captured small monsters being either Phlogiston- or Aether-subtypes, with those three being plain Anachronism-type monsters of neither subtype?
- (10) What is the probability that
*all thirty-one*captured small monsters are either Phlogiston- or Aether- subtypes, with no plain Anachronism-type monsters captured?

- (15) Let with . Characterize
*R*in terms of whether it is reflexive, irreflexive, symmetric, anti-symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. This is not a formal proof, but briefly explain your reasoning. - (15) Let with , that is,
*x*and*y*round up to the sane number. Characterize*R*in terms of whether it is reflexive, irreflexive, symmetric, anti-symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. This is not a formal proof, but briefly explain your reasoning. - (15) Let with ; that is, returns the square of rounded up. Characterize in terms of whether it is injective, surjective and/or bijective. This is not a formal proof, but briefly explain your reasoning.

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