Visual blocks for mathematical syntax

Below are some exercises for you to try.

These are just for practice, you will not receive any feedback about whether your answer is correct.

Q1. Convert the expression below into its contrapositive.

Q2. Negate the expression below.

Q3. The expression below states `*Every real number has a cube root*'.

Modify the statement to say that `*Every real number has a unique cube root*'.

Modify the statement to say that `

Q4. A student tried to write the statement `*if a real number is positive then its cube is positive*' in mathematical notation as follows:
\[
\forall x > 0 \implies x^3 > 0
\]
Is this correct? If not, what is wrong?

*Hint: could you construct the above using blocks?*

Construct a valid expression for this statement using blocks below.

Construct a valid expression for this statement using blocks below.

Q5. Recall that a sequence \(f\) is nondecreasing if \( \forall n \in \mathbb{N} \;\; f(n+1) \geq f(n) \);
it is nonincreasing if \( \forall n \in \mathbb{N} \;\; f(n+1) \leq f(n) \);
it is monotonic if it is nondecreasing or nonincreasing.
A student tried to write `*\(f\) is monotonic*' using blocks as below.
What is wrong with this? Fix it by constructing a correct expression for `*\(f\) is monotonic*'.

Q6. Consider the proverb "*All that glitters is not gold* ". A student expressed this using blocks as shown below.

Is this 'correct'? Does it

Is this 'correct'? Does it

- reflect the
*literal*meaning of the sentence? - capture the
*intended*meaning of the proverb? If not, modify the blocks so that it does.