Question

These statements are:R ⊃ (Q ∨ ∼ N) / Q ⊃ (U ⊃ ∼ B) / B ⊃ (N • U) / R • B

a.Inconsistent
b.Consistent

Answer 1

In consistent because statements q.. isn’t correct

Answer 2

The given statements are consistent.

Step-by-step explanation:

The given statements:

1. R ⊃ (Q ∨ ∼ N)
2. Q ⊃ (U ⊃ ∼ B)
3. B ⊃ (N • U)
4. R • B

To determine if these statements are consistent or inconsistent, we can use logical deduction.

We will assume that all the premises are true, and then check if the conclusion is also true. If we find any contradictions during the process, then the statements are inconsistent.

Let's go through the steps:

1. From 1st statement, we know that if R is true, then Q must be true or N must be false.
2. From 2nd statement, we know that if Q is true, then either U is false or B is false.
3. From 3rd statement, we know that if B is true, then both N and U must be true.
4. From the 4th statement, we know that both R and B are true.

Now, let's substitute the known values in the previous statements:

1. If R is true, then Q must be true or N must be false.
2. If Q is true, then either U is false or B is false.
3. If B is true, then both N and U must be true.
4. Both R and B are true.

From these statements, we can conclude that if R is true, then Q must be true or N must be false. Since R is true and N cannot be false, Q must be true.

Therefore, the given statements are consistent.