Let C Be the Unit Circle $x ^ { 2 } + y ^ { 2 } = 1$

question 31

True/False

Let C be the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ oriented in a counter-clockwise direction.Say whether the following statements are true or false.
If $\int_{c} \vec{H} \cdot d \vec{r}=0$ , we can conclude that $\vec { F }$ is path-independent field.

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Definitions:

Random Sample

A subset of individuals chosen from a larger population, where each member has an equal chance of being selected, ensuring the sample's representativeness.

Large Group

A social grouping that is too large for all members to maintain direct acquaintance and interaction, typically requiring formal structures for communication and decision-making.

Equal Chance

The principle that every individual or element in a sample or population has an identical likelihood of being chosen for something, commonly associated with random selection or assignment.

Government Food Vouchers

Financial assistance programs provided by governments to help low-income families purchase food and other essentials.