Final answer:
The law that shows the given logical propositions are equivalent is the Commutative law, which states that order does not affect the outcome of logical expressions involving 'and' and 'or'. This aligns with the mathematical understanding that elements can be rearranged without changing the result of the operation.
Step-by-step explanation:
The student asked which logical law shows that the two propositions r ^ (pVq) = r^(q V p) are logically equivalent. The correct choice is (d) Commutative law. This law states that you can change the order of the elements in a mathematical expression without changing the result.
For example, in arithmetic, 2 + 3 is the same as 3 + 2. Similarly, in logical expressions involving 'and' (^) and 'or' (V), the commutative law allows the operands to be swapped without changing the meaning or the outcome of the expression. Thus, pVq is logically equivalent to qVp. This question relates to logical expressions and the laws which govern them, typical for a high school level mathematics curriculum.
Other logical laws mentioned include the associative law, which refers to grouping of elements (e.g., (a + b) + c = a + (b + c)), and the distributive law, which combines both addition and multiplication in expressions (e.g., a * (b + c) = a * b + a * c). The commutative law specifically deals with the order of operations, making it the correct option for the given question on logical equivalence.