Both, depending on who is asking

Is a Tomato a Fruit or a Vegetable?

A tomato is a fruit to a botanist and a vegetable to a cook, and once a country's highest court had to decide.

Two words, two questions, both answered correctly.

Step 1 of 5

Botany asks where it came from.

In botany a fruit is whatever grows from a flower and carries the seeds. That makes tomatoes, cucumbers, peppers, beans and pumpkins all fruit.
Step 2 of 5

Cooking asks what it tastes like.

In a kitchen, fruit is sweet and comes at the end, and vegetables are savoury and come with the main course. By that test a tomato is plainly a vegetable.
Step 3 of 5

A court once had to rule on it.

In 1893 a tax on vegetables but not fruit sent the question to the American Supreme Court, which ruled that for tax purposes a tomato is a vegetable.
Step 4 of 5

Its savoury taste is real chemistry.

Tomatoes are unusually rich in the compounds behind savoury taste, which is why they turn up in almost every savoury cuisine and never in a fruit salad.
Step 5 of 5

Cold ruins them.

The damage does not reverse when it warms up again.

Below about twelve degrees a tomato stops making the compounds that give it its smell, and the damage does not reverse. A fridge genuinely spoils the flavour.

Tomatoes were treated with deep suspicion in Europe for two centuries, because they are related to some genuinely poisonous plants.

The short version

A tomato is a fruit by how it grew and a vegetable by how it is eaten, because the two words answer different questions.

Cut a tomato, a cucumber and a pepper. All three have seeds inside, and all three are fruit.