supply curve is the rising portion of marginal cost curve and above the minimum of average variable cost curve. do you agree

Yes, the above statement is true as supply curve is the rising portion of marginal cost curve over and above the average variable cost curve.

In a perfect competitive market, the following are the three profit maximising conditions. 
1. MR = MC 
2. MC is upward sloping
3.Price must be greater than or equal to minimum of SAVC curve at the equilibrium output 

Given these three conditions we can say that the firm will supply at any price that lies on the upward sloping part of the SMC and is greater than or equal to the minimum of SAVC. At a price below such a point the firm will not supply any quantity and will shut down production. Thus, it is only at the upward sloping part of MC that lies above the minimum point of SAVC that the firm will supply some quantity in the market.    

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