"If the interest rate of a bond is higher than the coupon rate of the bond, the market price of the bond is higher than the par value." True or false?

"For two bonds identical in every respect except the coupon rate, the price of the higher-coupon bond is less sensitive to the changes in interest rates than that of the lower-coupon bond; that is, the lower-coupon bond has a higher interest rate risk." True or false?