Use logical operators

(True && False) || !True

False

Or[And[True, False], Not[True]]

False

BooleanConvert[(a && b) || (!a && b)]

(a && b) || ( !a && b)

Resolve[ForAll[{a, b}, Equivalent[(a && b) || (!a && b), b]], {a, b}, Booleans]

Resolve[ForAll[{a, b}, (a && b) || ( !a && b) ⧦ b], {a, b}, Booleans]

Resolve[ForAll[a, Exists[b, (a && b) || (!a && b)]], {a, b}, Booleans]

Resolve[ForAll[a, Exists[b, (a && b) || ( !a && b)]], {a, b}, Booleans]

Resolve[ForAll[{a, b}, Implies[a && b, b]], {a, b}, Booleans]

Resolve[ForAll[{a, b}, Implies[a && b, b]], {a, b}, Booleans]

SatisfiableQ[(a && b) && (!a || !b), {a, b}]

False