$1.$ Translating fromordinary language. Express the followingwithout words, intermsofthestatementsPandQandthelogicalconnectives$,,,=,=,$or$.$ a$)$PnorQ$.$ b$)$PwhenQ$.$ c$)$P ifandonlyifQ. d$)$PexactlywhenQ$.$ e$)$P$.$Therefore,Q$.$ f$)$P isnecessaryforQ. g$)$P isnecessaryandsufficientforQ. h$)$PwheneverQ$.$ i$)$P$,$butnotQ. j$)$PunlessQ$.$