Practice Problems: CSE 173

Logic and Proofs

The below list is not exhaustive; you are requested not to restrict yourself only to these sets of practice problems.
We will update the list as needed.

From Kenneth H. Rosen, 7th edition

Topic Section Problems
Propositional Logic 1.1 9, 12, 14, 15, 19, 26, 27
Applications of Propositional Logic 1.2 7
Propositional Equivalence 1.2 7, 10, 12, 20, 24, 41
Predicates and Quantifiers 1.3 10, 14, 25, 37, 39, 40
Nested Quantifiers 1.4 6, 10, 16, 20, 24, 28, 32
Rules of Inference 1.5 3, 4, 6, 9, 16, 23, 24, 30
Introduction to Proofs 1.6 10, 15, 17, 27, 38, 41

From Kenneth H. Rosen (Indian Adaptation), 7th edition

Topic Section Problems
Propositional Logic 1.1 5, 8, 10, 11, 15, 22, 23, 47
Propositional Equivalence 1.2 7, 10, 12, 20, 24, 41
Predicates and Quantifiers 1.3 10, 14, 25, 37, 39, 40
Nested Quantifiers 1.4 6, 10, 16, 20, 24, 28, 32,
Rules of Inference 1.5 3, 4, 6, 9, 16, 23, 24, 30
Introduction to Proofs 1.6 10, 15, 17, 27, 38, 41

Problem 1:
For the following english argument, define the required propositions/predicates to translate  these into logic/argument form.
Finally, check if the argument form is valid.

All CSE 173 students are human.
Some CSE 173 students are travellers
------------------------------------
Some humans are logical travellers

Problem 2:
Prove that the below hypotheses lead to the conclusion:

If you send me a message in Piazza, then I will finish the of HW problem,
If you do not send me a message in Piazza, then I will go to bed early, and
If I go to bed early, then I will feel better,
-------------------------------------------------------------------------------
If I do not finish HW problem, then I will feel better.
Problem 3:
Prove that the following argument form is valid; use logical equivalence and rules of inferences done in class.

a disjuction b
a --> p
---------------------
q

Problem 4:
Prove the conclusion for a set of given premises: i) negation q, ii) p --> q, iii) negation p --> (s disjuntion q),
and a conclusion s.

Problem 5:
Prove that square root of 5 is irrational.

Problem 6:
Prove that the following argument form is valid; use logical equivalence and rules of inferences done in class.

a disjuntion b
a --> p
b --> p
----------------------
p

Functions, Sequence and Summations

From Kenneth H. Rosen, 7th edition

Topic Section Problems
Set 2.1 1, 14, 15, 19, 27, 32, 33, 40, 41, 44
Set operations 2.2 4, 12, 14, 16, 18, 26, 35, 36, 48
Functions 2.3 2, 12, 13, 15, 21, 23, 25, 30, 36, 38, 39
Sequence and Summations 2.4 6, 9, 12, 15, 26, 29, 30, 33, 34, 39, 40, 43
Cardinality of Sets 2.5 1, 2, 3, 4

Induction and Recursion

From Kenneth H. Rosen, 7th edition

Topic Section Problems
Mathematical Induction 5.1 3, 4, 5, 7, 16, 31
Strong induction 5.2 Optional
Recursion 5.3 3, 8, 12, 23, 24, 27