〜にしろ・〜にせよ
whether … or; even if; whatever
Noun / Plain form + にしろ / にせよ · A にしろ B にしろ
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にしろ and にせよ are formal versions of にしても (N3). They grant a point, then say it doesn't change the conclusion: 冗談にせよ、言っていいことと悪いことがある, "even as a joke, there are things you shouldn't say".
Doubled, they mean "whether … or": 行くにしろ行かないにしろ、連絡してください, "whether you go or not, let me know"; 肉にしろ魚にしろ, "whether it's meat or fish".
With question words, they mean "whatever": 理由は何にしろ, "whatever the reason".
The set phrase いずれにせよ means "either way, in any case", and is common in business and news. にしろ comes from the imperative of する, and にせよ from its written form.
Examples
行くにしろ行かないにしろ、連絡してください。
Whether you go or not, let me know.
冗談にせよ、言っていいことと悪いことがある。
Even as a joke, there are things you shouldn't say.
理由は何にしろ、遅刻はよくない。
Whatever the reason, being late isn't good.
いずれにせよ、明日までに決めなければならない。
Either way, we have to decide by tomorrow.
肉にしろ魚にしろ、新鮮なものがいい。
Whether it's meat or fish, fresh is best.