Determine whether the arguments are valid or invalid, and explain your answer in each case.
1) If anything is a trout, then it's a fish. A dolphin is not a fish. Therefore, a dolphin is not a trout.
(More statements to come...)
tweesers
Valid
To determine whether the argument is valid or invalid, we need to examine the logical structure of the statements. The argument consists of three statements:
1) If anything is a trout, then it's a fish.
2) A dolphin is not a fish.
3) Therefore, a dolphin is not a trout.
To analyze this argument, let's break it down:
Statement 1 establishes a conditional relationship: If something is a trout, then it is also a fish. This statement can be symbolized as "Trout → Fish". This is a valid conditional statement.
Statement 2 states that a dolphin is not a fish. This can be symbolized as "¬Fish(Dolphin)".
Statement 3 attempts to conclude that a dolphin is not a trout. However, this is not a valid conclusion because there is no direct logical relationship between being a fish and being a trout. The argument assumes that if something is not a fish, it cannot be a trout, which is not necessarily true.
Therefore, the argument is invalid. Just because a dolphin is not a fish does not necessarily mean it is not a trout. The conclusion is not logically supported by the premises.