MTH202 Quiz

Assignment# 01

MTH#202

Q1. Use symbols to write the logical --------------------------------------------?

Solution:

Let A = Alice is a manager B = Bob is a supervisor Premise 1: if Alice is a manager, then Bob is not a supervisor. A →¬B

Premise 2: if Bob is a supervisor, then Alice is not a manager. B →¬A

Conclusion: Alice is not a manager, and Bob is not a supervisor. ¬ A ^ ¬B

A

B

¬A ¬B A→ ¬B B → ¬A ¬A ^ ¬B

T · T · F · F · F · F · F T · F · F · T · T · T · F F · T · T · F · T · T · F F · F · T · T · T · T · T

Hence highlighted row all true so arguments is vailed.

Q2. Prove that A\ B = A ∩ Bc.

Solution:

Let x ∈ A \ B

By the definition of set difference. x ∈ A and x not belong to B By the definition of intersection.

Therefore, x ∈𝐴 and x not belong to B. So, x ∈𝐴 \ B Thus,

Conclusion:

Q3. Out of 80 students in a -----------------------------------------------------------------?

Solution:

• C: Students who attended the Coding session.
• D: Students who attended the Data Science session.
• M: Students who attended the Machine Learning session.

|C∩ D| = 30

|D ∩M| = 25 |C ∩M| = 20 |C ∩D ∩M| = 10 |C ∪D ∪M| = |D| +|M| - |C ∩ D| - |D∩ M| - |C∩ M| + |C∩ M| + |C∩ D∩ M|

80 = |C| + |D| + |M| - 30 – 25 –20 +10 2x + |M| = 145 ---------------------- (1) Here |M| = 20 + 25 – 10 = 35 Put |M| in eq 1