The following propositions are not valid in real life. Consider them just for this issue.
- Either the cat is a lawyer, or the dog is a priest.
- If a cat is a lawyer, then sofas are purple.
- Dog is a priest.
- Sofas are purple.
Regarding the above propositions, it can be stated that:
A) All propositions are true and complementary.
B) Proposition (2) does not admit that Proposition (4) is true.
C) Proposition (4) does not admit that Proposition (2) is true.
D) Propositions (3) and (4) cannot be true at the same time.
I believe it should be a biconditional in 2. If dogs are priests by the XOR of $(1)$, cats are not lawyers. If it were a biconditional in $(2)$, sofas would not be purple if and only if cats were not lawyers. Thus, as we cited the XOR of $(1)$ that cats are not lawyers, sofas would not be purple, which is a contradiction to the fact that $(4)$ is true.That would give $(D)$ as an answer
The following propositions are not valid in real life. Consider them just for this issue.
Every duck is football.
If any doll is a bottle, then some bottles are roofed.
Every roof is football.
If some pens are balls, then every doll is a bottle.
Check the alternative that respects all the established logical premises:
A) As some pens are balls, then there are bottles that are football.
B) If no doll is a bottle, then some bottles are roofed.
C) Since no duck is football, all pens are balls.
D) If some pens are not balls, no roof is football.
In question 2, is demonstrating the validity of an argument that has the alternative proposition as a conclusion sufficient?