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## Here's the Solution to this Question

Question 1:

Let

A = “I study data structure”,

B = “I study Bioinformatics”,

C = “I study programming”,

D = “I study discrete math”

a. The formula for the statement “I study Bioinformatics if I study programming and discrete math” is $C\land D\to B.$

b. The formula for the statement “I cannot study data structure when I do not study programming or discrete math” is $\neg(C\lor D)\to\neg A.$

c. The formula for the statement “I study data structure if and only if I do not study Bioinformatics” is $A\leftrightarrow \neg B.$

Question 2:

Let’s consider a propositional language where

$p$ means “Paola is happy”,

$q$ means “Paola paints a picture”,

$r$ means “Renzo is happy”.

Let us write English statement that corresponds to the following compound propositions:

1. The formula $p ∧ q → ¬ r$ corresponds to the English statement: "If Paola is happy and she paints a picture, then Renzo is not happy".
2. The formula $¬ (p ∧ ¬q)=¬ p \lor q$ correspons to the English statements: "It is not true that Paola is happy and she does not paint a picture" and "Paola is not happy or she paints a picture".