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7. Countability For the problem, let R[0, 1] denote the reals in the interval [0, 1]. 1. For a countable set S, the set [0, 1] x S is countable. O True OFalse 2. The set R[0, 1]2 = R[0, 1] x IR[0, 1] has the same cardinality as the set R[0, 1]. True OFalse 3. For a countable set S, the set R[0, 1] x S has the same cardinality as IR[0, 1]. O True OFalse 4. For an n x n matrix A all of whose entries are 0 or 1, describe an n bit string that is not any row of the matrix. Use the notation ali, j] for the jth entry in the ith row and the notation bli, j] to be the complement of the bit ali, j]. (An example of an n bit string in the matrix which is a[1, 1], a[1, 2], ..., a[1, m] which is the first row of the matrix and a[1, 1], b[1, 2], ..., a[1, m] is a different n bit string as they differ in the second bit.)