Sets

Step 1: Formula for remaining mass.
The formula for the remaining mass after time given the half-life period is: Where is the initial mass and is the time elapsed.
Step 2: Apply the formula.
Given that mg, days, and days, we substitute into the formula:
Step 3: Conclusion.
Thus, the mass remaining after 50 days is mg, corresponding to option (C).

Step 1: Find the elements of set A.
The prime numbers between 0 and 9 are . Therefore, set .
Step 2: Calculate the number of elements in the power set.
The number of elements in the power set of a set with elements is . Since the set has 4 elements, the power set has elements.
Step 3: Conclusion.
Thus, the number of elements in the power set of is 16, corresponding to option (C).

We are tasked with simplifying the logical expression:

Step 1: Apply Distribution: First, we apply the distributive property to . Using the distributive property of conjunction over disjunction, we get: So, the expression becomes:

Step 2: Simplify the Negation: Now, simplify the negation . By applying De Morgan's law to the negation, we get: So the expression becomes:

Step 3: Combine Like Terms: Notice that appears twice. So we can eliminate the redundancy: Now, we can group terms to simplify further:

Step 4: Final Simplification: Finally, we can simplify further by observing that the expression is equivalent to: This is the simplified version of the given logical expression.

Final Answer: Therefore, the equivalent of the given expression is: