Final answer:
If two equal forces are applied to a cart in opposite directions, the cart will remain at rest if it was initially at rest, or continue in motion without any change in speed or direction if it was initially moving.
Step-by-step explanation:
When person X pushes a cart with a certain force and person Y pushes the cart with an equal force but in the opposite direction, the effects on the cart follow Newton's laws of motion. According to Newton's first law, an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. In this case, the forces from person X and Y are equal and opposite, therefore they cancel out each other leading to a net force of zero. This implies that if the cart was initially at rest, it will remain at rest. If the cart was in motion, it will continue in motion without any change in its speed or direction. Hence the answer to your question is: a) It brings the cart to rest if it was initially at rest.
Learn more about Newton's laws of motion