Question 7

Explanation

We can simplify the statements into mathematical logic forms.

Variable Definitions

Let:

• $p$: $A = B$
• $q$: $C \neq D$
• $r$: $E = F$
• $s$: $G = H$

Translating Statements

1. Statement 1: $A = B$ or $C \neq D$

   $$p \lor q$$

   This form is equivalent to the implication: $\sim p \to q$.

2. Statement 2: If $E = F$ then $G = H$

   $$r \to s$$

   This form is equivalent to the contrapositive: $\sim s \to \sim r$.

3. Statement 3: $C = D$ or $G \neq H$

   Note that $C = D$ is the negation of $q$ ($\sim q$), and $G \neq H$ is the negation of $s$ ($\sim s$).

   $$\sim q \lor \sim s$$

   This form is equivalent to the implication: $q \to \sim s$.

Drawing Conclusion

We have the following logical chain:

1. From Statement 1: $\sim p \to q$
2. From Statement 3: $q \to \sim s$
3. From Statement 2: $\sim s \to \sim r$

Using syllogism, we can combine all three:

The final result is $\sim p \to \sim r$. This implication form is equivalent to a disjunction (or):

Translating Back to Sentences

• $p$ is $A = B$
• $\sim r$ is $E \neq F$

So the conclusion is: $A = B$ or $E \neq F$.