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For each of the following sets, determine whether they are countable or uncountable (explain your reasoning)....

For each of the following sets, determine whether they are countable or uncountable (explain your reasoning). For countable sets, provide some explicit counting scheme and list the first 20 elements according to your scheme. (a) The set [0, 1]R × [0, 1]R = {(x, y) | x, y ∈ R, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

(b) The set [0, 1]Q × [0, 1]Q = {(x, y) | x, y ∈ Q, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

(c) The set [0, 1]Q × [0, 1]R = {(x, y) | x ∈ Q, y ∈ R, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

(d) The set N × N × N = {(a, b, c) | a, b, c ∈ N}.

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