If the proposition 'No frogs are amphibians' is given as false then which of the following

propositions can be immediately inferred to be true?

The correct option is Some frogs are amphibians.

To understand why this proposition is immediately inferred to be true, we can analyze the relationship between the two categorical propositions using the classical Square of Opposition in logic.
Categorical propositions are structured in four standard forms:
1. A proposition (Universal Affirmative): "All frogs are amphibians."
2. E proposition (Universal Negative): "No frogs are amphibians."
3. I proposition (Particular Affirmative): "Some frogs are amphibians."
4. O proposition (Particular Negative): "Some frogs are not amphibians."

According to the Square of Opposition, the diagonal relation between E ("No S is P") and I ("Some S is P") is one of contradiction. Contradictory propositions always have opposite truth values:
- If the E proposition is true, then the I proposition must be false.
- If the E proposition is false, then the I proposition must be true.

In this problem, we are given that the E proposition ("No frogs are amphibians") is false.
Because the I proposition is its contradiction, the truth value of the I proposition ("Some frogs are amphibians") must be the exact opposite. Therefore, "Some frogs are amphibians" can be immediately inferred to be true.