Relations and Functions: common misconceptions

If your child says… “Swapping the entries keeps the same pair.”

Ask together

Is 2 less than 1?

What’s true

Reversing different entries makes a different ordered pair, even if both belong to the relation.

If your child says… “Transitive means every pair has its reverse.”

Ask together

Which arrow joins the start and end of the chain through b?

What’s true

Transitivity requires a direct pair joining the ends of every two-link chain.

If your child says… “A different chosen number means a different class.”

Ask together

Which group changes when you point to 3 instead of 1?

What’s true

Related numbers name the same class, including themselves.

If your child says… “Four possible pairs means four relations.”

Ask together

For each pair, can you choose either to keep it or leave it out?

What’s true

Multiply the set sizes to count pairs, then double once for each pair.

If your child says… “One output for each input means one-one.”

Ask together

Does giving each input one output prevent two inputs from sharing that output?

What’s true

One-one requires different inputs to have different outputs.

If your child says… “A doubling formula can reach any real number.”

Ask together

What sign would an input need to produce a negative target?

What’s true

A target counts as reached only when its required input belongs to the domain.

If your child says… “One-one is enough for every function to be bijective.”

Ask together

When natural numbers are doubled, which inputs could reach odd numbers?

What’s true

One-one guarantees onto between equally sized finite sets, but this can fail for infinite sets.

If your child says… “The function written first acts first.”

Ask together

Which function acts directly on x inside the brackets?

What’s true

In g composed with f, f acts first and g receives its result.