Let m be the statement "x is perpendicular to M," and let n be the statement "x is perpendicular to N." Express each of the following statements in symbols.
(a) x is perpendicular to N but not perpendicular to M.
(b) x is not perpendicular to M, nor is it perpendicular to N.
(c) x is perpendicular to N only if x is perpendicular to M.
(d) x is not perpendicular to N provided it is perpendicular to M.
(e) It is not the case that x is perpendicular to M and perpendicular to N.
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