Q1real09sol-1

# Q1real09sol-1 - CSE303 Q1 SOLUTIONS Summer 2009 PART 1...

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Unformatted text preview: CSE303 Q1 SOLUTIONS Summer 2009 PART 1: YES/NO QUESTIONS Circle the correct answer. Write SHORT justification. 1. 2 { 1 , 2 } ∩ { 1 , 2 } 6 = ∅ Justify : { 1 , 2 } ⊆ { 1 , 2 } i.e. { 1 , 2 } ∈ 2 { 1 , 2 } . y 2. Some R ⊆ A × B are functions that map A into B . Justify : Functions are special type of relations. y 3. If A is uncountable, then | A | = | R | ( R is the set of real numbers). Justify : 2 R is uncountable, but | R | < | 2 R | by Cantor Theorem. n 4. For any function f from A onto A , f ( a ) 6 = a . Justify : Identity function: f ( x ) = x for all x ∈ A maps A onto A . n 5. {{ a,b }} ∈ 2 { a,b, { a,b }} Justify : {{ a,b }} ⊆ { a,b, { a,b }} . y 6. Let Σ = { n ∈ N : n ≤ 1 } . There are infinitely many finite languages over Σ. Justify : Σ = { , 1 } and Σ ? is countably infinite. The set of all finite subsets of any countably infinite set is countably infinite. y 7. L + = { w 1 ...w n : w i ∈ L,i = 1 , 2 ,..n,n ≥ 1 } . Justify :definition y 8. Regular language is a regular expression....
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Q1real09sol-1 - CSE303 Q1 SOLUTIONS Summer 2009 PART 1...

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