Let the original price be x. After a 25% discount, the price is x - 0.25x = 0.75x. So, 0.75x = 30, thus x = 40.

The conclusion is not valid because not all birds can fly; penguins are an exception.

The conclusion does not logically follow from the premises.

The conclusion follows logically from the premises. If all cats are animals and some animals are not dogs, it implies that there are cats that are not dogs.

Since all cats are animals and some animals are not dogs, it follows that some cats must not be dogs.

Since all cats are mammals and some mammals are not dogs, it follows that some cats must not be dogs.

Since some animals are not pets, it follows that some dogs must not be pets.

Since all dogs are pets and some pets are not cats, it can be inferred that some pets are dogs.

Since all dogs are pets and some pets are not cats, it can be concluded that some dogs are not cats.

The conclusion is valid because if all dogs bark and some pets are dogs, then those pets must bark.

The conclusion is not valid because it contradicts the premise that all fruits are healthy.

Since all humans are mortal and Socrates is a human, it follows that Socrates is mortal.

Since all mammals are warm-blooded and some warm-blooded animals are not birds, it can be concluded that some mammals are not birds.

Since all mammals are warm-blooded and some warm-blooded animals can fly, it can be concluded that some mammals can fly.

The conclusion is valid because if all mammals have hearts and some whales are mammals, then those whales must have hearts.

The conclusion is not valid. While all roses are flowers, it does not necessarily follow that some roses are red.

Since all roses are flowers and some flowers fade quickly, it can be concluded that some flowers are not roses.

Since all roses are flowers, but not all flowers are roses, it can be concluded that some flowers are not roses.

The conclusion is not valid. The premises do not provide enough information to conclude that some squares are not blue.

Since all squares are rectangles and some rectangles are not cubes, it can be inferred that some squares are not cubes.

Since all squares are rectangles and some rectangles are not cubes, it can be concluded that some squares are not cubes.

Since all squares are rectangles and some rectangles are not squares, it is valid to conclude that some rectangles are not squares.

The conclusion is valid because if all students are learners and some learners are not teachers, then some students must not be teachers.

Bark is the outer covering of a tree, just as skin is the outer covering of a body.

Begin and start are synonyms, just as end and finish are synonyms.

Birds fly, and fish swim. The relationship is based on the primary mode of movement.

A bird lives in a nest, just as a fish lives in an aquarium.

Bitter and sweet are opposites, just as hot and cold are opposites.

Bitter and sweet are opposites, just as sharp and dull are opposites.

Bitter and sweet are opposites, just as sour and sweet are opposites.