Step 1: Understanding the Concept:
Sterilization methods are terminal (permanent) contraceptive methods that prevent the transport of gametes through surgical intervention.
Step 2: Detailed Explanation:
X (Male Method): In a vasectomy, a small part of the vas deferens is removed or tied up through a small incision on the scrotum.
Y (Female Method): In a tubectomy, a small part of the fallopian tubes is removed or tied up through a small incision in the abdomen or through the vagina.
Both methods are nearly 100% effective but have very poor reversibility.
Step 3: Final Answer:
X is Vasectomy and Y is Tubectomy.