# Write out the conclusion that follows in a single step from…

Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe): 1. (S U F) • ( F U B) 2. S v F 3.

To derive a conclusion from the given premises, we need to apply logical reasoning and make inferences based on the rules of propositional logic. Let’s analyze the premises and determine the possible conclusion.

Premise 1 states: (S U F) • (F U B)
Premise 2 states: S v F

In order to derive a conclusion, we can start by examining premise 1. The statement (S U F) • (F U B) consists of two disjunctions connected by a conjunction. Let’s break it down and focus on each disjunction separately:

Disjunction 1: (S U F)
Disjunction 2: (F U B)

In disjunction 1, we have (S U F), which can be read as “S implies F” or “If S, then F.” This represents a conditional statement, where S is the antecedent and F is the consequent.

In disjunction 2, we have (F U B), which can be read as “F implies B” or “If F, then B.” Again, this represents a conditional statement, where F is the antecedent and B is the consequent.

Now, let’s consider premise 2, which states S v F. This can be read as “S or F,” meaning that either S is true or F is true. This represents a disjunction, where S and F are the two possible options.

To derive a conclusion, we need to combine the information from the premises and determine the logical relationship between the statements. The key is to recognize any patterns or dependencies that exist.

By analyzing the premises, we can see that there is a connection between S and F. Premise 2 states that either S or F is true. In premise 1, we have the conditional statements (S U F) and (F U B), which suggest that S and F are related. The logical relationship can be interpreted as:

If S is true, then F is true.
If F is true, then B is true.

Now, let’s consider three possible cases:

Case 1: S is true and F is true (S,F)
In this case, since S is true, based on the conditional statement (S U F), F must also be true. Thus, both conditions in premise 1 are satisfied.
Therefore, the conclusion can be derived as:
S v F

Case 2: S is true and F is false (S,~F)
In this case, since S is true, based on the conditional statement (S U F), F would also have to be true. However, this contradicts the assumption that F is false.
Therefore, this case is not possible.

Case 3: S is false and F is true (~S,F)
In this case, since F is true, based on the conditional statement (F U B), B must also be true. Thus, both conditions in premise 1 are satisfied.
Therefore, the conclusion can be derived as:
S v F

Based on the analysis of the premises and possible cases, the conclusion that can be derived is:

(S v F)

This conclusion states that either S is true or F is true.